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801
help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:38:30
What is the behaviour of $n\mapsto \sqrt{n+100} - \sqrt{n}$?
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
510,789,298,321,096,700
TeXit
02/21/2022 11:38:32
**Guilhem**
https://cdn.discordapp.c…321877995526.png
688329321877995526.png
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:39:16
Oupsie, I didn't mean to interrupt 🌼
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help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 11:39:18
Whats mapsto?
1
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help-10
aeb6e91318fb4adfa044352ee7763f86
332,849,454,753,251,300
sucka mah
02/21/2022 11:39:30
nonono just continue onwards, you didn't interrupt
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:39:48
Don't you see the LaTeX?
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help-10
aeb6e91318fb4adfa044352ee7763f86
332,849,454,753,251,300
sucka mah
02/21/2022 11:39:49
I am the one who answered without being allowed to😈
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:40:10
This
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:41:27
I don't think integrals are appropriate here... What is $(-1)^t$ where $t\in \mathbb{R}$?
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
510,789,298,321,096,700
TeXit
02/21/2022 11:41:30
**Guilhem**
https://cdn.discordapp.c…321877995526.png
688329321877995526.png
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help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 11:41:33
Uh i dont know that notation sorry
1
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:42:09
Well I have a bot that makes things look nice
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help-10
aeb6e91318fb4adfa044352ee7763f86
332,849,454,753,251,300
sucka mah
02/21/2022 11:42:11
do you not see the bot message from TeXit BOT
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aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 11:42:34
I dont know that symbol from the bot bro
1
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:42:48
Ahhhhh d'accord
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:43:08
The sequence $(\sqrt{n+100} - \sqrt{n})$ !
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help-10
aeb6e91318fb4adfa044352ee7763f86
510,789,298,321,096,700
TeXit
02/21/2022 11:43:10
**Guilhem**
https://cdn.discordapp.c…321877995526.png
688329321877995526.png
0
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Guilhem
7949
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:43:32
Does it increase, decrease, converges... ?
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1
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:43:53
*s
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 11:44:30
It decreases i think
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help-10
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Mat
02/21/2022 11:45:07
,align \func{f}{&\mathbb{N}}{\mathbb{R}} \\ & n \mapsto f(n) = \sqrt{n+100} - \sqrt{n}
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help-10
aeb6e91318fb4adfa044352ee7763f86
510,789,298,321,096,700
TeXit
02/21/2022 11:45:09
**Mat**
https://cdn.discordapp.c…466631987211.png
551807466631987211.png
0
1
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:45:16
Nice !
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help-10
aeb6e91318fb4adfa044352ee7763f86
551,807,466,631,987,200
Mat
02/21/2022 11:45:23
It's a symbol used for functions!
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 11:45:30
Ok
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Deleted User
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:45:46
No.
0
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sucka mah
5404
sucka mah
false
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:46:23
It is often simpler to use functions. What is the behaviour of $f(t) = \sqrt{t+100} - \sqrt{t}$ ?
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
510,789,298,321,096,700
TeXit
02/21/2022 11:46:25
**Guilhem**
https://cdn.discordapp.c…321877995526.png
688329321877995526.png
0
1
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 11:46:32
If we rationalize this then i think it should be decreasing
1
0
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 11:47:38
Its coming decreasing for me
1
0
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:48:26
oh yeah !!!
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:48:33
My mistake
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 11:48:39
Ok
1
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:49:20
So?
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:49:38
What is its limit?
0
1
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 11:50:37
Zero
1
0
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:51:28
Yes. So what is the behaviour of your series?
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Mat
9616
Mat
false
801
help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 11:51:49
So my series will be increasing
1
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Deleted User
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 11:51:59
Tending to infinity
1
0
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 11:52:16
Is that correct?
1
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:52:34
Allas, there is an oscillation due to $(-1)^n$ !
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help-10
aeb6e91318fb4adfa044352ee7763f86
510,789,298,321,096,700
TeXit
02/21/2022 11:52:36
**Guilhem**
https://cdn.discordapp.c…321877995526.png
688329321877995526.png
0
1
688,329,321,877,995,500
Guilhem
7949
Guilhem
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 11:52:49
Yes
1
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:54:57
So the behaviour isn't obvious
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 11:56:01
Maybe the oscillation is not enough prevent the series from going to infinity, maybe it is just perfect to make it converge...
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 11:56:22
Yes
1
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
551,807,466,631,987,200
Mat
02/21/2022 11:59:34
$\sum a_n $ converges $\implies \lim_{n \rightarrow \infty} a_n = 0$
0
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
510,789,298,321,096,700
TeXit
02/21/2022 11:59:36
**Mat**
https://cdn.discordapp.c…466631987211.png
551807466631987211.png
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688,329,321,877,995,500
Guilhem
7949
Guilhem
false
801
help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 12:00:16
Exactly!
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help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 12:00:40
Yea
1
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 12:00:43
So in fact the jump at each step if too big to have a convergent series !
0
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 12:01:07
How do we know that?
1
0
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 12:01:56
Because the terms go to infinity, so each step, the series makes a big 'jump'
0
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 12:02:40
So it cannot converge to a finite value, because otherwise it would oscillate around
0
1
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 12:03:07
But far around
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
551,807,466,631,987,200
Mat
02/21/2022 12:03:53
The implication above is equivalent to \\ (It is not true that $\lim_{n \rightarrow \infty} a_n = 0$ ) $\implies \sum a_n $ does not converge
0
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
510,789,298,321,096,700
TeXit
02/21/2022 12:04:44
**Mat**
https://cdn.discordapp.c…466631987211.png
551807466631987211.png
0
1
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 12:05:33
How?
1
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 12:06:03
Why would it oscillate far around?
1
0
null
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 12:08:50
Because, for example, the terms will be greater than $1$ after a certain $n$. Each step, you add or subtract a certain quantity depending of the sign of $(-1)^n$. So, after some time, you begin to jump more than one unit left and right in turns
0
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
510,789,298,321,096,700
TeXit
02/21/2022 12:08:53
**Guilhem**
https://cdn.discordapp.c…321877995526.png
688329321877995526.png
0
1
null
null
null
null
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 12:09:22
This violent change of direction makes it impossible to converge!
0
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 12:09:41
idk if this is clear 🥳
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 12:11:10
If the series was convergent to a certain limit $l$, it would not leave the segment $[l-1/2 ; l+1/2]$ after some time. But we've shown that it does!
0
1
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
510,789,298,321,096,700
TeXit
02/21/2022 12:11:12
**Guilhem**
https://cdn.discordapp.c…321877995526.png
688329321877995526.png
0
1
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801
help-10
aeb6e91318fb4adfa044352ee7763f86
688,329,321,877,995,500
Guilhem
02/21/2022 12:11:31
.
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 12:12:53
Oooh
1
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 12:12:55
Ok
1
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 12:13:02
Got it
1
0
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help-10
aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 12:13:06
Thank you
1
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help-10
aeb6e91318fb4adfa044352ee7763f86
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Guilhem
02/21/2022 12:13:22
Derien, c'est toujours un grand plaisir !
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help-10
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456,226,577,798,135,800
Deleted User
02/21/2022 12:13:31
?
1
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help-10
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688,329,321,877,995,500
Guilhem
02/21/2022 12:14:20
You are welcome!
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Mat
02/21/2022 12:14:57
Ahah even more obscure than LaTex
0
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Mat
02/21/2022 12:15:08
.
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aeb6e91318fb4adfa044352ee7763f86
456,226,577,798,135,800
Deleted User
02/21/2022 12:15:25
Haha it was french I got it now
1
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help-10
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551,807,466,631,987,200
Mat
02/21/2022 12:15:33
Lol
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260,073,142,553,280,500
JCtheMC
11/07/2021 12:51:32
https://cdn.discordapp.c…8020/unknown.png
unknown.png
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2c03308bf887441c93bcb6f146d271a8
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JCtheMC
11/07/2021 12:51:48
i'm trying to formulate a formula for this one
1
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help-10
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JCtheMC
11/07/2021 12:52:16
so, the first person that draws has a probability of (n-1)/n to not draw their own name
1
0
null
null
null
null
null
802
help-10
2c03308bf887441c93bcb6f146d271a8
260,073,142,553,280,500
JCtheMC
11/07/2021 12:53:06
but the person after that has a probability of (n-2)/(n-1) - the probability that their name has already been drawn
1
0
null
null
null
null
null
802
help-10
2c03308bf887441c93bcb6f146d271a8
260,073,142,553,280,500
JCtheMC
11/07/2021 12:53:07
and so on
1
0
null
null
null
null
null
802
help-10
2c03308bf887441c93bcb6f146d271a8
260,073,142,553,280,500
JCtheMC
11/07/2021 12:53:56
am i on the right track with that train of thought and if so, can someone give me a hint how to express this part in a formula "the probability that their name has already been drawn"
1
0
null
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null
802
help-10
2c03308bf887441c93bcb6f146d271a8
140,928,979,849,838,600
Plurmorant
11/07/2021 12:57:09
wrong track, that probability is too complicated
0
1
null
null
null
null
null
802
help-10
2c03308bf887441c93bcb6f146d271a8
140,928,979,849,838,600
Plurmorant
11/07/2021 12:57:16
are there questions after a. and b.?
0
1
null
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null
null
null
802
help-10
2c03308bf887441c93bcb6f146d271a8
260,073,142,553,280,500
JCtheMC
11/07/2021 12:57:29
yes but we don;t have to do them
1
0
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802
help-10
2c03308bf887441c93bcb6f146d271a8
260,073,142,553,280,500
JCtheMC
11/07/2021 12:57:56
c.) Consecutively, find a general formula for arbitrary values of n.
1
0
688,329,321,877,995,500
Guilhem
7949
Guilhem
false
802
help-10
2c03308bf887441c93bcb6f146d271a8
260,073,142,553,280,500
JCtheMC
11/07/2021 12:58:02
that's the last one
1
0
688,329,321,877,995,500
Guilhem
7949
Guilhem
false
802
help-10
2c03308bf887441c93bcb6f146d271a8
888,859,319,024,648,200
james_ash
11/07/2021 12:58:09
you might wanna take a look at derangement
0
1
null
null
null
null
null
802
help-10
2c03308bf887441c93bcb6f146d271a8
140,928,979,849,838,600
Plurmorant
11/07/2021 12:59:00
it's a nasty formula with the principle of inclusion/exclusion if you feel like learning that
0
1
null
null
null
null
null
802
help-10
2c03308bf887441c93bcb6f146d271a8
260,073,142,553,280,500
JCtheMC
11/07/2021 12:59:11
not really
1
0
null
null
null
null
null
802
help-10
2c03308bf887441c93bcb6f146d271a8
260,073,142,553,280,500
JCtheMC
11/07/2021 12:59:29
this is part of the set of problems for the class where they teach us about conditional probability
1
0
null
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null
null
802
help-10
2c03308bf887441c93bcb6f146d271a8
140,928,979,849,838,600
Plurmorant
11/07/2021 13:00:29
for b. just list all the ways it can happen and divide by the total
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1
null
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802
help-10
2c03308bf887441c93bcb6f146d271a8
140,928,979,849,838,600
Plurmorant
11/07/2021 13:00:40
you can't really get the answer by multiplying things
0
1
null
null
null
null
null
802
help-10
2c03308bf887441c93bcb6f146d271a8
260,073,142,553,280,500
JCtheMC
11/07/2021 13:01:46
i've thought about this one for a while and i just can't get beyond the first probability before things get complicated
1
0
null
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802
help-10
2c03308bf887441c93bcb6f146d271a8
140,928,979,849,838,600
Plurmorant
11/07/2021 13:02:15
what do you mean?
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1
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802
help-10
2c03308bf887441c93bcb6f146d271a8
260,073,142,553,280,500
JCtheMC
11/07/2021 13:03:35
ok the probability that the first person to draw DOESN'T draw their own name is n-1/n
1
0
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help-10
2c03308bf887441c93bcb6f146d271a8
260,073,142,553,280,500
JCtheMC
11/07/2021 13:03:50
but then, i have no clue how to move on
1
0
null
null
null
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null
802
help-10
2c03308bf887441c93bcb6f146d271a8
260,073,142,553,280,500
JCtheMC
11/07/2021 13:04:09
because obviously the first person could draw the 2nd persons name, so the probability of them drawing their own name goes to 0
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0
null
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802
help-10
2c03308bf887441c93bcb6f146d271a8
260,073,142,553,280,500
JCtheMC
11/07/2021 13:17:34
so when you say that i should list all the ways it can happen... i don't know what to do really
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