mikeion/dissertation_data_with_split · Datasets at Hugging Face

conversation_id int64 1 206k	help_channel stringlengths 6 7	__rowid__ stringlengths 32 32	author_id int64 62,061,868B 1,071,443,446B	author_name stringlengths 2 32	timestamp stringlengths 19 19	content stringlengths 0 3.97k	url stringlengths 0 591	fileName stringlengths 0 513	student int64 0 1	helper int64 0 1	references.id float64 62,061,868B 1,071,056,124B ⌀	references.name stringlengths 2 32 ⌀	references.discriminator stringlengths 4 4 ⌀	references.nickname stringlengths 1 32 ⌀	references.isBot bool 2 classes
335	help-10	5781eaee71324a4e9b78c3e1e943e668	209,767,680,100,663,300	Kaisheng21	10/29/2021 09:11:31	and 3 * -1			0	1	null	null	null	null	null
335	help-10	5781eaee71324a4e9b78c3e1e943e668	209,767,680,100,663,300	Kaisheng21	10/29/2021 09:11:33	so it doesn't work			0	1	null	null	null	null	null
335	help-10	5781eaee71324a4e9b78c3e1e943e668	507,116,799,284,740,100	EpicGuy4227	10/29/2021 09:11:56	b = 0			0	1	null	null	null	null	null
335	help-10	5781eaee71324a4e9b78c3e1e943e668	507,116,799,284,740,100	EpicGuy4227	10/29/2021 09:12:26	RHS becomes 0 so try like b = 1			0	1	null	null	null	null	null
335	help-10	5781eaee71324a4e9b78c3e1e943e668	209,767,680,100,663,300	Kaisheng21	10/29/2021 09:12:32	what			0	1	null	null	null	null	null
335	help-10	5781eaee71324a4e9b78c3e1e943e668	507,116,799,284,740,100	EpicGuy4227	10/29/2021 09:12:35	and c = -2			0	1	null	null	null	null	null
335	help-10	5781eaee71324a4e9b78c3e1e943e668	209,767,680,100,663,300	Kaisheng21	10/29/2021 09:12:35	what are you on about			0	1	null	null	null	null	null
335	help-10	5781eaee71324a4e9b78c3e1e943e668	209,767,680,100,663,300	Kaisheng21	10/29/2021 09:12:44	wait fuck			0	1	null	null	null	null	null
335	help-10	5781eaee71324a4e9b78c3e1e943e668	209,767,680,100,663,300	Kaisheng21	10/29/2021 09:12:45	yes			0	1	null	null	null	null	null
335	help-10	5781eaee71324a4e9b78c3e1e943e668	209,767,680,100,663,300	Kaisheng21	10/29/2021 09:12:46	you're right			0	1	null	null	null	null	null
335	help-10	5781eaee71324a4e9b78c3e1e943e668	209,767,680,100,663,300	Kaisheng21	10/29/2021 09:12:50	ok			0	1	null	null	null	null	null
335	help-10	5781eaee71324a4e9b78c3e1e943e668	373,980,725,721,956,350	DEOG	10/29/2021 09:13:21	thanks			1	0	null	null	null	null	null
335	help-10	5781eaee71324a4e9b78c3e1e943e668	209,767,680,100,663,300	Kaisheng21	10/29/2021 09:13:28	wait			0	1	null	null	null	null	null
335	help-10	5781eaee71324a4e9b78c3e1e943e668	373,980,725,721,956,350	DEOG	10/29/2021 09:13:28	.close			1	0	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	507,977,331,722,289,150	KentyMcDclr8	11/05/2021 04:18:47	i'm kinda stuck on how to find the sum of this, i've proven that it is convergent using the alternating series test. to find the sum, i made it into a telescoping series but it's alternating and that's been messing with me.	https://cdn.discordapp.c…0859/unknown.png	unknown.png	1	0	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	507,977,331,722,289,150	KentyMcDclr8	11/05/2021 04:34:22	@Helpers any kind souls wanna nudge me in the right direction here?			1	0	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 04:36:03	may i suggest grouping the terms into pairs?			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 04:36:16	your series is absolutely convergent, so grouping will not mess anything up			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 04:36:50	the general idea is that $\sum_{n=2}^{\infty} (-1)^n a_n = \sum_{k=1}^{\infty} (a_{2k} - a_{2k+1})$			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	510,789,298,321,096,700	TeXit	11/05/2021 04:36:53	Ann	https://cdn.discordapp.c…144404037632.png	183668144404037632.png	0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 04:37:11	it might be a good idea to decompose 3/(n^2 + n - 2) into partial fractions first, just in case			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	507,977,331,722,289,150	KentyMcDclr8	11/05/2021 04:41:12	ah ok, so i should group the even and odd terms and then see what i get? i'll try that			1	0	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	507,977,331,722,289,150	KentyMcDclr8	11/05/2021 04:49:49	even with the grouping, either i'm doing something severely wrong, or using the wrong method, none of my terms cancel out			1	0	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	507,977,331,722,289,150	KentyMcDclr8	11/05/2021 04:53:19	$\frac{3}{n^2+n-2}=\frac{1}{n-1}-\frac{1}{n+2}$			1	0	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	510,789,298,321,096,700	TeXit	11/05/2021 04:53:32	KentyMcDclr8	https://cdn.discordapp.c…331722289176.png	507977331722289176.png	0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	507,977,331,722,289,150	KentyMcDclr8	11/05/2021 04:55:23	i get this but can't seem to go further			1	0	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 04:56:32	well now you have $$\sum_{k=1}^{\infty} \frac{1}{2k-1} - \frac{1}{2k+2} - \paren{\frac{1}{2k+1-1} - \frac{1}{2k+1+2}}$$ in accordance with that formula i wrote earlier			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	510,789,298,321,096,700	TeXit	11/05/2021 04:56:35	Ann	https://cdn.discordapp.c…144404037632.png	183668144404037632.png	0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	507,977,331,722,289,150	KentyMcDclr8	11/05/2021 05:04:32	what would be the continuation of that because i'm still stuck even after making the last 2 denominators 2k and 2k + 3?			1	0	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 05:16:05	$\sum_{k=1}^{\infty} \frac{1}{2k-1} + \frac{1}{2k+3} - \frac{1}{2k+2} - \frac{1}{2k}$			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	510,789,298,321,096,700	TeXit	11/05/2021 05:16:07	Ann	https://cdn.discordapp.c…144404037632.png	183668144404037632.png	0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 05:16:08	hmm			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 05:16:18	i think i might've painted us into a bit of a corner here			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 05:16:20	:thonk:			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	507,977,331,722,289,150	KentyMcDclr8	11/05/2021 05:18:39	nothing cancels out =/			1	0	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 05:23:16	hence my last remark.			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 05:23:27	full disclosure, i did not quite see this coming.			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	507,977,331,722,289,150	KentyMcDclr8	11/05/2021 05:34:46	haha, all good			1	0	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 05:35:32	let's throw this into WA			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 05:35:42	,w sum[n=2, infty] (-1)^n * 3/(n^2 + n - 2)			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	510,789,298,321,096,700	TeXit	11/05/2021 05:35:47	Results provided by WolframAlpha			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 05:35:49	:thonk:			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 05:35:50	log			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 05:35:52	:thonk::thonk:			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 05:36:08	hm			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 05:36:11	what if...			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 05:36:33	what if we consider $f(x) = \sum_{n=2}^{\infty} \frac{3x^n}{(n+2)(n-1)}$?			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	510,789,298,321,096,700	TeXit	11/05/2021 05:36:36	Ann	https://cdn.discordapp.c…144404037632.png	183668144404037632.png	0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	183,668,144,404,037,630	Ann	11/05/2021 05:37:05	then our series will be the value of f(-1), and maybe we can glean some information about the function this way...			0	1	null	null	null	null	null
336	help-10	e555fcd0c22246998f0a20da6220c15d	507,977,331,722,289,150	KentyMcDclr8	11/05/2021 05:41:30	hmm			1	0	null	null	null	null	null
337	help-10	7e5073d6036d4aa49aa0207716df6229	582,935,438,260,699,100	𝙨𝙖𝙙 𝙗𝙤𝙞	01/28/2022 05:15:35	how did it become that?			1	0	null	null	null	null	null
337	help-10	7e5073d6036d4aa49aa0207716df6229	582,935,438,260,699,100	𝙨𝙖𝙙 𝙗𝙤𝙞	01/28/2022 05:15:36		https://cdn.discordapp.c…D7A487244233.jpg	6F1DA09F-5467-4C26-815F-D7A487244233.jpg	1	0	null	null	null	null	null
337	help-10	7e5073d6036d4aa49aa0207716df6229	582,935,438,260,699,100	𝙨𝙖𝙙 𝙗𝙤𝙞	01/28/2022 05:15:53	Can someone give me the step by step explanation please			1	0	null	null	null	null	null
337	help-10	7e5073d6036d4aa49aa0207716df6229	706,934,233,012,371,600	Ansh_	01/28/2022 05:18:53	You know about De Moivre's theorem? or roots of sin x > 1 existing in complex numbers in general?			0	1	null	null	null	null	null
337	help-10	7e5073d6036d4aa49aa0207716df6229	706,934,233,012,371,600	Ansh_	01/28/2022 05:19:06	Or are you just curious about it :o			0	1	null	null	null	null	null
337	help-10	7e5073d6036d4aa49aa0207716df6229	582,935,438,260,699,100	𝙨𝙖𝙙 𝙗𝙤𝙞	01/28/2022 05:20:54	curious			1	0	null	null	null	null	null
337	help-10	7e5073d6036d4aa49aa0207716df6229	706,934,233,012,371,600	Ansh_	01/28/2022 05:21:58	https://brilliant.org/wiki/de-moivres-theorem/			0	1	null	null	null	null	null
337	help-10	7e5073d6036d4aa49aa0207716df6229	706,934,233,012,371,600	Ansh_	01/28/2022 05:22:03	A good short read imo			0	1	null	null	null	null	null
337	help-10	7e5073d6036d4aa49aa0207716df6229	582,935,438,260,699,100	𝙨𝙖𝙙 𝙗𝙤𝙞	01/28/2022 05:22:20	thank you so much			1	0	582,935,438,260,699,100	𝙨𝙖𝙙 𝙗𝙤𝙞	9609	𝙨𝙖𝙙 𝙗𝙤𝙞	false
337	help-10	7e5073d6036d4aa49aa0207716df6229	706,934,233,012,371,600	Ansh_	01/28/2022 05:23:59	From there, you can directly write $[e^{ix} - e^{-ix}] = 2i \sqrt{\frac{4}{3}}$ and solve using the normal methods			0	1	null	null	null	null	null
337	help-10	7e5073d6036d4aa49aa0207716df6229	510,789,298,321,096,700	TeXit	01/28/2022 05:24:25	Ansh	https://cdn.discordapp.c…233012371577.png	706934233012371577.png	0	1	null	null	null	null	null
337	help-10	7e5073d6036d4aa49aa0207716df6229	582,935,438,260,699,100	𝙨𝙖𝙙 𝙗𝙤𝙞	01/28/2022 05:24:59	thanks so much			1	0	null	null	null	null	null
337	help-10	7e5073d6036d4aa49aa0207716df6229	582,935,438,260,699,100	𝙨𝙖𝙙 𝙗𝙤𝙞	01/28/2022 05:25:02	.close			1	0	null	null	null	null	null
338	help-10	f0e4860627834800866c1a42b308eb81	765,399,107,199,041,500	Pratik Saha	01/28/2022 05:43:16	@Helpers			1	0	null	null	null	null	null
338	help-10	f0e4860627834800866c1a42b308eb81	755,831,671,588,126,700	RepliedPencil	01/28/2022 05:50:53	What I always do is extract as much data as possible from the given question, and work around with the data.			0	1	null	null	null	null	null
338	help-10	f0e4860627834800866c1a42b308eb81	755,831,671,588,126,700	RepliedPencil	01/28/2022 05:51:05	We know $x, y \in \bN$			0	1	null	null	null	null	null
338	help-10	f0e4860627834800866c1a42b308eb81	510,789,298,321,096,700	TeXit	01/28/2022 05:51:07	Pencil	https://cdn.discordapp.c…671588126784.png	755831671588126784.png	0	1	null	null	null	null	null
338	help-10	f0e4860627834800866c1a42b308eb81	755,831,671,588,126,700	RepliedPencil	01/28/2022 05:51:38	@Pratik Saha read the question and say what happens next			0	1	null	null	null	null	null
338	help-10	f0e4860627834800866c1a42b308eb81	765,399,107,199,041,500	Pratik Saha	01/28/2022 05:52:22	If we divide by 4 remains a remainder			1	0	null	null	null	null	null
338	help-10	f0e4860627834800866c1a42b308eb81	765,399,107,199,041,500	Pratik Saha	01/28/2022 05:52:38	If we divide with 7 remains a remainder			1	0	null	null	null	null	null
338	help-10	f0e4860627834800866c1a42b308eb81	755,831,671,588,126,700	RepliedPencil	01/28/2022 05:52:52	It leaves a remainder*			0	1	null	null	null	null	null
338	help-10	f0e4860627834800866c1a42b308eb81	765,399,107,199,041,500	Pratik Saha	01/28/2022 05:53:06	What is the largest value of A+B			1	0	null	null	null	null	null
338	help-10	f0e4860627834800866c1a42b308eb81	755,831,671,588,126,700	RepliedPencil	01/28/2022 05:53:08	Can you write it in terms of x and a for this			0	1	765,399,107,199,041,500	Pratik Saha	5086	Pratik Saha	false
338	help-10	f0e4860627834800866c1a42b308eb81	755,831,671,588,126,700	RepliedPencil	01/28/2022 05:53:19	And in terms of y and b for this			0	1	null	null	null	null	null
338	help-10	f0e4860627834800866c1a42b308eb81	755,831,671,588,126,700	RepliedPencil	01/28/2022 05:54:02	@Pratik Saha			0	1	null	null	null	null	null
338	help-10	f0e4860627834800866c1a42b308eb81	869,532,694,688,706,600	EpsilonNought	01/28/2022 05:54:34	@Pratik Saha I suggest using modular arithmetic for this			0	1	null	null	null	null	null
338	help-10	f0e4860627834800866c1a42b308eb81	150,414,892,225,134,600	RokettoJanpu	01/28/2022 05:55:13	i muted this for the remaning duration too			0	1	null	null	null	null	null
338	help-10	f0e4860627834800866c1a42b308eb81	150,414,892,225,134,600	RokettoJanpu	01/28/2022 05:55:16	.close			0	1	765,399,107,199,041,500	Pratik Saha	5086	Pratik Saha	false
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	706,934,233,012,371,600	Ansh_	01/28/2022 05:55:43	Sorry for the confusion Jintaro ^^"			1	0	765,399,107,199,041,500	Pratik Saha	5086	Pratik Saha	false
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	715,915,261,634,674,800	cdat.icp ∞	01/28/2022 06:07:48	Hi! The problem Im struggling is in the picture. I've done thins until now and I think its correct:	https://cdn.discordapp.c…_at_11.59.38.png	Screen_Shot_2022-01-25_at_11.59.38.png	0	1	765,399,107,199,041,500	Pratik Saha	5086	Pratik Saha	false
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	715,915,261,634,674,800	cdat.icp ∞	01/28/2022 06:07:59	i. the reason it's wrong is that the author assumes that A and B are "served" by the same upper bound - which they might not be  a value of M that works as a bound for A may not work for B  you need to have two different bounds, one for A and one for B, and to then take their maximum for the upper bound of A \cup B			0	1	765,399,107,199,041,500	Pratik Saha	5086	Pratik Saha	false
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	715,915,261,634,674,800	cdat.icp ∞	01/28/2022 06:08:04	however for ii			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	715,915,261,634,674,800	cdat.icp ∞	01/28/2022 06:08:34	I havent been thought how to write proofs yet and this is my first assignment so I'm scared to mess it up			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	715,915,261,634,674,800	cdat.icp ∞	01/28/2022 06:08:47	how would I write it correctly if my answer for i is correct?			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	569,167,697,925,898,240	Camilleone	01/28/2022 06:10:06	sounds like a troll			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	569,167,697,925,898,240	Camilleone	01/28/2022 06:10:12	anyway			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	569,167,697,925,898,240	Camilleone	01/28/2022 06:10:15	back to this question			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	715,915,261,634,674,800	cdat.icp ∞	01/28/2022 06:10:18	oh ok			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	569,167,697,925,898,240	Camilleone	01/28/2022 06:10:34	you're right, A and B might have different bounds			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	569,167,697,925,898,240	Camilleone	01/28/2022 06:10:39	say, M_1 and M_2			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	569,167,697,925,898,240	Camilleone	01/28/2022 06:11:14	and you also rightly said you should take the maximum for the UB of A\cup B			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	569,167,697,925,898,240	Camilleone	01/28/2022 06:11:45	so, that's $M = \max\{M_1, M_2\}$			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	510,789,298,321,096,700	TeXit	01/28/2022 06:11:47	Camilleone	https://cdn.discordapp.c…697925898261.png	569167697925898261.png	0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	569,167,697,925,898,240	Camilleone	01/28/2022 06:12:29	can you see how to continue?			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	715,915,261,634,674,800	cdat.icp ∞	01/28/2022 06:13:47	Well i mean once I know this I can write why this would make the proof wrong but the problem is idk how to put it into 'math language'			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	569,167,697,925,898,240	Camilleone	01/28/2022 06:14:20	ah i see, so you need help rephrasing (i)?			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	715,915,261,634,674,800	cdat.icp ∞	01/28/2022 06:14:37	yes exactly!			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	715,915,261,634,674,800	cdat.icp ∞	01/28/2022 06:14:57	this helps thought to start. I hadnt even thought about writing it this way			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	569,167,697,925,898,240	Camilleone	01/28/2022 06:16:17	well, you can do something like saying that the definition of Cinderella liking a set only means that there exists such an M such that (copy the definition), but this M may differ for each set			0	1	null	null	null	null	null
339	help-10	93a6dbae91974b8aaca6a30eb6987bfb	569,167,697,925,898,240	Camilleone	01/28/2022 06:16:49	so there is no reason to assume that the same value of M will work for both sets A and B simultaneously			0	1	null	null	null	null	null

335

help-10

5781eaee71324a4e9b78c3e1e943e668

209,767,680,100,663,300

Kaisheng21

10/29/2021 09:11:31

and 3 * -1

0

1

null

335

help-10

5781eaee71324a4e9b78c3e1e943e668

209,767,680,100,663,300

Kaisheng21

10/29/2021 09:11:33

so it doesn't work

0

1

null

335

help-10

5781eaee71324a4e9b78c3e1e943e668

507,116,799,284,740,100

EpicGuy4227

10/29/2021 09:11:56

b = 0

0

1

null

335

help-10

5781eaee71324a4e9b78c3e1e943e668

507,116,799,284,740,100

EpicGuy4227

10/29/2021 09:12:26

RHS becomes 0 so try like b = 1

0

1

null

335

help-10

5781eaee71324a4e9b78c3e1e943e668

209,767,680,100,663,300

Kaisheng21

10/29/2021 09:12:32

what

0

1

null

335

help-10

5781eaee71324a4e9b78c3e1e943e668

507,116,799,284,740,100

EpicGuy4227

10/29/2021 09:12:35

and c = -2

0

1

null

335

help-10

5781eaee71324a4e9b78c3e1e943e668

209,767,680,100,663,300

Kaisheng21

10/29/2021 09:12:35

what are you on about

0

1

null

335

help-10

5781eaee71324a4e9b78c3e1e943e668

209,767,680,100,663,300

Kaisheng21

10/29/2021 09:12:44

wait fuck

0

1

null

335

help-10

5781eaee71324a4e9b78c3e1e943e668

209,767,680,100,663,300

Kaisheng21

10/29/2021 09:12:45

yes

0

1

null

335

help-10

5781eaee71324a4e9b78c3e1e943e668

209,767,680,100,663,300

Kaisheng21

10/29/2021 09:12:46

you're right

0

1

null

335

help-10

5781eaee71324a4e9b78c3e1e943e668

209,767,680,100,663,300

Kaisheng21

10/29/2021 09:12:50

ok

0

1

null

335

help-10

5781eaee71324a4e9b78c3e1e943e668

373,980,725,721,956,350

DEOG

10/29/2021 09:13:21

thanks

1

0

null

335

help-10

5781eaee71324a4e9b78c3e1e943e668

209,767,680,100,663,300

Kaisheng21

10/29/2021 09:13:28

wait

0

1

null

335

help-10

5781eaee71324a4e9b78c3e1e943e668

373,980,725,721,956,350

DEOG

10/29/2021 09:13:28

.close

1

0

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

507,977,331,722,289,150

KentyMcDclr8

11/05/2021 04:18:47

i'm kinda stuck on how to find the sum of this, i've proven that it is convergent using the alternating series test. to find the sum, i made it into a telescoping series but it's alternating and that's been messing with me.

https://cdn.discordapp.c…0859/unknown.png

unknown.png

1

0

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

507,977,331,722,289,150

KentyMcDclr8

11/05/2021 04:34:22

@Helpers any kind souls wanna nudge me in the right direction here?

1

0

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 04:36:03

may i suggest grouping the terms into pairs?

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 04:36:16

your series is absolutely convergent, so grouping will not mess anything up

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 04:36:50

the general idea is that $\sum_{n=2}^{\infty} (-1)^n a_n = \sum_{k=1}^{\infty} (a_{2k} - a_{2k+1})$

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

510,789,298,321,096,700

TeXit

11/05/2021 04:36:53

**Ann**

https://cdn.discordapp.c…144404037632.png

183668144404037632.png

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 04:37:11

it might be a good idea to decompose 3/(n^2 + n - 2) into partial fractions first, just in case

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

507,977,331,722,289,150

KentyMcDclr8

11/05/2021 04:41:12

ah ok, so i should group the even and odd terms and then see what i get? i'll try that

1

0

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

507,977,331,722,289,150

KentyMcDclr8

11/05/2021 04:49:49

even with the grouping, either i'm doing something severely wrong, or using the wrong method, none of my terms cancel out

1

0

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

507,977,331,722,289,150

KentyMcDclr8

11/05/2021 04:53:19

$\frac{3}{n^2+n-2}=\frac{1}{n-1}-\frac{1}{n+2}$

1

0

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

510,789,298,321,096,700

TeXit

11/05/2021 04:53:32

**KentyMcDclr8**

https://cdn.discordapp.c…331722289176.png

507977331722289176.png

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

507,977,331,722,289,150

KentyMcDclr8

11/05/2021 04:55:23

i get this but can't seem to go further

1

0

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 04:56:32

well now you have $$\sum_{k=1}^{\infty} \frac{1}{2k-1} - \frac{1}{2k+2} - \paren{\frac{1}{2k+1-1} - \frac{1}{2k+1+2}}$$ in accordance with that formula i wrote earlier

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

510,789,298,321,096,700

TeXit

11/05/2021 04:56:35

**Ann**

https://cdn.discordapp.c…144404037632.png

183668144404037632.png

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

507,977,331,722,289,150

KentyMcDclr8

11/05/2021 05:04:32

what would be the continuation of that because i'm still stuck even after making the last 2 denominators 2k and 2k + 3?

1

0

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 05:16:05

$\sum_{k=1}^{\infty} \frac{1}{2k-1} + \frac{1}{2k+3} - \frac{1}{2k+2} - \frac{1}{2k}$

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

510,789,298,321,096,700

TeXit

11/05/2021 05:16:07

**Ann**

https://cdn.discordapp.c…144404037632.png

183668144404037632.png

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 05:16:08

hmm

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 05:16:18

i think i might've painted us into a bit of a corner here

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 05:16:20

:thonk:

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

507,977,331,722,289,150

KentyMcDclr8

11/05/2021 05:18:39

nothing cancels out =/

1

0

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 05:23:16

hence my last remark.

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 05:23:27

full disclosure, i did not quite see this coming.

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

507,977,331,722,289,150

KentyMcDclr8

11/05/2021 05:34:46

haha, all good

1

0

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 05:35:32

let's throw this into WA

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 05:35:42

,w sum[n=2, infty] (-1)^n * 3/(n^2 + n - 2)

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

510,789,298,321,096,700

TeXit

11/05/2021 05:35:47

Results provided by WolframAlpha

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 05:35:49

:thonk:

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 05:35:50

log

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 05:35:52

:thonk::thonk:

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 05:36:08

hm

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 05:36:11

what if...

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 05:36:33

what if we consider $f(x) = \sum_{n=2}^{\infty} \frac{3x^n}{(n+2)(n-1)}$?

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

510,789,298,321,096,700

TeXit

11/05/2021 05:36:36

**Ann**

https://cdn.discordapp.c…144404037632.png

183668144404037632.png

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

183,668,144,404,037,630

Ann

11/05/2021 05:37:05

then our series will be the value of f(-1), and maybe we can glean some information about the function this way...

0

1

null

336

help-10

e555fcd0c22246998f0a20da6220c15d

507,977,331,722,289,150

KentyMcDclr8

11/05/2021 05:41:30

hmm

1

0

null

337

help-10

7e5073d6036d4aa49aa0207716df6229

582,935,438,260,699,100

𝙨𝙖𝙙 𝙗𝙤𝙞

01/28/2022 05:15:35

how did it become that?

1

0

null

337

help-10

7e5073d6036d4aa49aa0207716df6229

582,935,438,260,699,100

𝙨𝙖𝙙 𝙗𝙤𝙞

01/28/2022 05:15:36

https://cdn.discordapp.c…D7A487244233.jpg

6F1DA09F-5467-4C26-815F-D7A487244233.jpg

1

0

null

337

help-10

7e5073d6036d4aa49aa0207716df6229

582,935,438,260,699,100

𝙨𝙖𝙙 𝙗𝙤𝙞

01/28/2022 05:15:53

Can someone give me the step by step explanation please

1

0

null

337

help-10

7e5073d6036d4aa49aa0207716df6229

706,934,233,012,371,600

Ansh_

01/28/2022 05:18:53

You know about De Moivre's theorem? or roots of sin x > 1 existing in complex numbers in general?

0

1

null

337

help-10

7e5073d6036d4aa49aa0207716df6229

706,934,233,012,371,600

Ansh_

01/28/2022 05:19:06

Or are you just curious about it :o

0

1

null

337

help-10

7e5073d6036d4aa49aa0207716df6229

582,935,438,260,699,100

𝙨𝙖𝙙 𝙗𝙤𝙞

01/28/2022 05:20:54

curious

1

0

null

337

help-10

7e5073d6036d4aa49aa0207716df6229

706,934,233,012,371,600

Ansh_

01/28/2022 05:21:58

https://brilliant.org/wiki/de-moivres-theorem/

0

1

null

337

help-10

7e5073d6036d4aa49aa0207716df6229

706,934,233,012,371,600

Ansh_

01/28/2022 05:22:03

A good short read imo

0

1

null

337

help-10

7e5073d6036d4aa49aa0207716df6229

582,935,438,260,699,100

𝙨𝙖𝙙 𝙗𝙤𝙞

01/28/2022 05:22:20

thank you so much

1

0

582,935,438,260,699,100

𝙨𝙖𝙙 𝙗𝙤𝙞

9609

𝙨𝙖𝙙 𝙗𝙤𝙞

false

337

help-10

7e5073d6036d4aa49aa0207716df6229

706,934,233,012,371,600

Ansh_

01/28/2022 05:23:59

From there, you can directly write $[e^{ix} - e^{-ix}] = 2i \sqrt{\frac{4}{3}}$ and solve using the normal methods

0

1

null

337

help-10

7e5073d6036d4aa49aa0207716df6229

510,789,298,321,096,700

TeXit

01/28/2022 05:24:25

**Ansh**

https://cdn.discordapp.c…233012371577.png

706934233012371577.png

0

1

null

337

help-10

7e5073d6036d4aa49aa0207716df6229

582,935,438,260,699,100

𝙨𝙖𝙙 𝙗𝙤𝙞

01/28/2022 05:24:59

thanks so much

1

0

null

337

help-10

7e5073d6036d4aa49aa0207716df6229

582,935,438,260,699,100

𝙨𝙖𝙙 𝙗𝙤𝙞

01/28/2022 05:25:02

.close

1

0

null

338

help-10

f0e4860627834800866c1a42b308eb81

765,399,107,199,041,500

Pratik Saha

01/28/2022 05:43:16

@Helpers

1

0

null

338

help-10

f0e4860627834800866c1a42b308eb81

755,831,671,588,126,700

RepliedPencil

01/28/2022 05:50:53

What I always do is extract as much data as possible from the given question, and work around with the data.

0

1

null

338

help-10

f0e4860627834800866c1a42b308eb81

755,831,671,588,126,700

RepliedPencil

01/28/2022 05:51:05

We know $x, y \in \bN$

0

1

null

338

help-10

f0e4860627834800866c1a42b308eb81

510,789,298,321,096,700

TeXit

01/28/2022 05:51:07

**Pencil**

https://cdn.discordapp.c…671588126784.png

755831671588126784.png

0

1

null

338

help-10

f0e4860627834800866c1a42b308eb81

755,831,671,588,126,700

RepliedPencil

01/28/2022 05:51:38

@Pratik Saha read the question and say what happens next

0

1

null

338

help-10

f0e4860627834800866c1a42b308eb81

765,399,107,199,041,500

Pratik Saha

01/28/2022 05:52:22

If we divide by 4 remains a remainder

1

0

null

338

help-10

f0e4860627834800866c1a42b308eb81

765,399,107,199,041,500

Pratik Saha

01/28/2022 05:52:38

If we divide with 7 remains a remainder

1

0

null

338

help-10

f0e4860627834800866c1a42b308eb81

755,831,671,588,126,700

RepliedPencil

01/28/2022 05:52:52

It **leaves** a remainder*

0

1

null

338

help-10

f0e4860627834800866c1a42b308eb81

765,399,107,199,041,500

Pratik Saha

01/28/2022 05:53:06

What is the largest value of **A+B**

1

0

null

338

help-10

f0e4860627834800866c1a42b308eb81

755,831,671,588,126,700

RepliedPencil

01/28/2022 05:53:08

Can you write it in terms of x and a for this

0

1

765,399,107,199,041,500

Pratik Saha

5086

Pratik Saha

false

338

help-10

f0e4860627834800866c1a42b308eb81

755,831,671,588,126,700

RepliedPencil

01/28/2022 05:53:19

And in terms of y and b for this

0

1

null

338

help-10

f0e4860627834800866c1a42b308eb81

755,831,671,588,126,700

RepliedPencil

01/28/2022 05:54:02

@Pratik Saha

0

1

null

338

help-10

f0e4860627834800866c1a42b308eb81

869,532,694,688,706,600

EpsilonNought

01/28/2022 05:54:34

@Pratik Saha I suggest using modular arithmetic for this

0

1

null

338

help-10

f0e4860627834800866c1a42b308eb81

150,414,892,225,134,600

RokettoJanpu

01/28/2022 05:55:13

i muted this for the remaning duration too

0

1

null

338

help-10

f0e4860627834800866c1a42b308eb81

150,414,892,225,134,600

RokettoJanpu

01/28/2022 05:55:16

.close

0

1

765,399,107,199,041,500

Pratik Saha

5086

Pratik Saha

false

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

706,934,233,012,371,600

Ansh_

01/28/2022 05:55:43

Sorry for the confusion Jintaro ^^"

1

0

765,399,107,199,041,500

Pratik Saha

5086

Pratik Saha

false

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

715,915,261,634,674,800

cdat.icp ∞

01/28/2022 06:07:48

Hi! The problem Im struggling is in the picture. I've done thins until now and I think its correct:

https://cdn.discordapp.c…_at_11.59.38.png

Screen_Shot_2022-01-25_at_11.59.38.png

0

1

765,399,107,199,041,500

Pratik Saha

5086

Pratik Saha

false

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

715,915,261,634,674,800

cdat.icp ∞

01/28/2022 06:07:59

i. the reason it's wrong is that the author assumes that A and B are "served" by the same upper bound - which they might not be  a value of M that works as a bound for A may not work for B  you need to have two different bounds, one for A and one for B, and to then take their maximum for the upper bound of A \cup B

0

1

765,399,107,199,041,500

Pratik Saha

5086

Pratik Saha

false

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

715,915,261,634,674,800

cdat.icp ∞

01/28/2022 06:08:04

however for ii

0

1

null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

715,915,261,634,674,800

cdat.icp ∞

01/28/2022 06:08:34

I havent been thought how to write proofs yet and this is my first assignment so I'm scared to mess it up

0

1

null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

715,915,261,634,674,800

cdat.icp ∞

01/28/2022 06:08:47

how would I write it correctly if my answer for i is correct?

0

1

null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

569,167,697,925,898,240

Camilleone

01/28/2022 06:10:06

sounds like a troll

0

1

null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

569,167,697,925,898,240

Camilleone

01/28/2022 06:10:12

anyway

0

1

null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

569,167,697,925,898,240

Camilleone

01/28/2022 06:10:15

back to this question

0

1

null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

715,915,261,634,674,800

cdat.icp ∞

01/28/2022 06:10:18

oh ok

0

1

null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

569,167,697,925,898,240

Camilleone

01/28/2022 06:10:34

you're right, A and B might have different bounds

0

1

null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

569,167,697,925,898,240

Camilleone

01/28/2022 06:10:39

say, M_1 and M_2

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1

null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

569,167,697,925,898,240

Camilleone

01/28/2022 06:11:14

and you also rightly said you should take the maximum for the UB of A\cup B

0

1

null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

569,167,697,925,898,240

Camilleone

01/28/2022 06:11:45

so, that's $M = \max\{M_1, M_2\}$

0

1

null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

510,789,298,321,096,700

TeXit

01/28/2022 06:11:47

**Camilleone**

https://cdn.discordapp.c…697925898261.png

569167697925898261.png

0

1

null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

569,167,697,925,898,240

Camilleone

01/28/2022 06:12:29

can you see how to continue?

0

1

null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

715,915,261,634,674,800

cdat.icp ∞

01/28/2022 06:13:47

Well i mean once I know this I can write why this would make the proof wrong but the problem is idk how to put it into 'math language'

0

1

null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

569,167,697,925,898,240

Camilleone

01/28/2022 06:14:20

ah i see, so you need help rephrasing (i)?

0

1

null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

715,915,261,634,674,800

cdat.icp ∞

01/28/2022 06:14:37

yes exactly!

0

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null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

715,915,261,634,674,800

cdat.icp ∞

01/28/2022 06:14:57

this helps thought to start. I hadnt even thought about writing it this way

0

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null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

569,167,697,925,898,240

Camilleone

01/28/2022 06:16:17

well, you can do something like saying that the definition of Cinderella liking a set only means that there exists such an M such that (copy the definition), but this M may differ for each set

0

1

null

339

help-10

93a6dbae91974b8aaca6a30eb6987bfb

569,167,697,925,898,240

Camilleone

01/28/2022 06:16:49

so there is no reason to assume that the same value of M will work for both sets A and B simultaneously

0

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null