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help-10
502468ffd7d745e68abd3f4958fdeca6
251,854,584,597,708,800
PapaBread
10/29/2021 17:19:54
n=1 11111 01111 One switch
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help-10
502468ffd7d745e68abd3f4958fdeca6
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PapaBread
10/29/2021 17:20:34
n=2 11111 00111 Two switches
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help-10
502468ffd7d745e68abd3f4958fdeca6
251,854,584,597,708,800
PapaBread
10/29/2021 17:22:03
n=3 11111 01111 01011 11011 10011 00011 Six switches
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help-10
502468ffd7d745e68abd3f4958fdeca6
251,854,584,597,708,800
PapaBread
10/29/2021 17:27:33
n=4 11111 10111 00111 00101 10101 11101 01101 01001 11001 10001 00001 Eleven switches
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help-10
502468ffd7d745e68abd3f4958fdeca6
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PapaBread
10/29/2021 17:28:42
It kinda looks like it adds on 2 more to the rate each time
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help-10
502468ffd7d745e68abd3f4958fdeca6
185,214,393,749,995,520
gg
10/29/2021 17:33:47
So because the rate of change was 5 switches when n=4 when n=5 the rate of change will be 7 switches and so n=5 Eighteen switches?
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373,884,980,977,336,300
Remavas
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Remavas
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PapaBread
10/29/2021 17:34:16
Thats my thinking
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Zanarcane
6798
what is a manifold?
false
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help-10
502468ffd7d745e68abd3f4958fdeca6
185,214,393,749,995,520
gg
10/29/2021 17:36:02
So could the recurrence relation be described as something like: a(n) = [a(n-1) - a(n-2)] + 2 ?
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help-10
502468ffd7d745e68abd3f4958fdeca6
185,214,393,749,995,520
gg
10/29/2021 17:37:06
Wait
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help-10
502468ffd7d745e68abd3f4958fdeca6
185,214,393,749,995,520
gg
10/29/2021 17:37:49
I think it would be a(n) = a(n-1) + [a(n-1) - a(n-2)] + 2
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help-10
502468ffd7d745e68abd3f4958fdeca6
185,214,393,749,995,520
gg
10/29/2021 17:38:47
YEAH THATS IT
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help-10
502468ffd7d745e68abd3f4958fdeca6
185,214,393,749,995,520
gg
10/29/2021 17:38:49
THANK YOU
1
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help-10
502468ffd7d745e68abd3f4958fdeca6
251,854,584,597,708,800
PapaBread
10/29/2021 17:39:21
Epic
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help-10
502468ffd7d745e68abd3f4958fdeca6
185,214,393,749,995,520
gg
10/29/2021 17:39:38
.close
1
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:26:29
https://cdn.discordapp.c…9426/unknown.png
unknown.png
1
0
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:26:43
How did we get from the top line to the bottom line
1
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help-10
e267d99acbad4917963cf258e3459345
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reking
11/11/2021 14:27:20
through the middle line? 😄
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:28:16
hi
1
0
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:35:55
Are you still there?
1
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help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 14:36:46
yes
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:37:09
oh ok
1
0
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help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 14:37:36
i just dont know what the question is, there is a line between top and bottom that you asked about? where exactly are you unclear
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:38:17
I meant
1
0
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help-10
e267d99acbad4917963cf258e3459345
477,823,425,893,629,950
kattunge
11/11/2021 14:38:19
....
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:38:37
im getting confused
1
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:39:06
im asking how did the top line equal the second line
1
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help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 14:43:55
well for example, the first part becomes $$\frac{81}{n^4}\left( \frac{n(n+1)}{2} \right)^2 = \frac{81}{4n^4} n^2(n+1)^2$$ $$ = \frac{81}{4n^2} (n+1)^2 = \frac{81}{4} \left( \frac{n+1}{n} \right)^2 $$ $$ = \frac{81}{4} \left( 1 + \frac{1}{n} \right)^2 $$
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help-10
e267d99acbad4917963cf258e3459345
652,336,711,325,712,400
quantum
11/11/2021 14:43:58
for the first term, they changed 1/n^4 into 1/(n^2)^2
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help-10
e267d99acbad4917963cf258e3459345
510,789,298,321,096,700
TeXit
11/11/2021 14:43:58
**reking**
https://cdn.discordapp.c…388548141059.png
123486388548141059.png
0
1
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:46:03
because of an LCD between the 2 expressions
1
0
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:46:05
for step 2?
1
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help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 14:46:52
you mean the n^4 and the n^2 is cancelling out?
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:47:32
I meant that a 4 appears in the denominator of 81
1
0
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help-10
e267d99acbad4917963cf258e3459345
652,336,711,325,712,400
quantum
11/11/2021 14:48:17
they just switched the denominators
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help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 14:48:31
it comes from the 2 in the denominator at the beginning
0
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help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 14:48:40
it is squared, so i can take it outside and it becomes 4
0
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help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 14:49:19
$\left( \frac{1}{2} \right)^2 = \frac{1}{4}$
0
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help-10
e267d99acbad4917963cf258e3459345
510,789,298,321,096,700
TeXit
11/11/2021 14:49:23
**reking**
https://cdn.discordapp.c…388548141059.png
123486388548141059.png
0
1
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:51:20
lol
1
0
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:52:07
im lost
1
0
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:52:31
I understand the denominator in the expression is squared. That its denominator will equal 4
1
0
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:53:51
ok
1
0
null
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:53:52
so
1
0
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:54:28
the denominators are multiplied giving 81/4n^4
1
0
null
null
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:54:38
n^2 is cancelled out
1
0
null
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:54:46
leaving 81/4n^2
1
0
null
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:55:28
(n+1)^2 = (n+1)(n+1) = n^2 +2n +1
1
0
null
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:56:37
81/4n^2 = 81/4 because n^2 is now canceled
1
0
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1,669
help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 14:56:43
there is no need to multiply that out
0
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1,669
help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 14:56:59
you can just move the n^2 inside
0
1
null
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1,669
help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 14:57:35
$\frac{1}{n^2} \left( n+1 \right)^2 = \left( \frac{n+1}{n} \right) ^2$
0
1
null
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1,669
help-10
e267d99acbad4917963cf258e3459345
510,789,298,321,096,700
TeXit
11/11/2021 14:57:37
**reking**
https://cdn.discordapp.c…388548141059.png
123486388548141059.png
0
1
null
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1,669
help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 14:58:39
because.. well $\left(\frac{A}{B} \right)^2 = \frac{A^2}{B^2}$
0
1
null
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1,669
help-10
e267d99acbad4917963cf258e3459345
510,789,298,321,096,700
TeXit
11/11/2021 14:58:54
**reking**
https://cdn.discordapp.c…388548141059.png
123486388548141059.png
0
1
null
null
null
null
null
1,669
help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 14:59:11
you see??
0
1
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:59:31
yes
1
0
null
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null
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 14:59:56
(n+1)^2 / n^2 = (n+1 / n )^2
1
0
null
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null
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:00:27
I'm sorry, I forgot a lot of basic math skills
1
0
null
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:00:58
going from step 2 to step 3
1
0
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help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 15:04:05
yes? or ?
0
1
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:04:15
how?
1
0
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:04:31
what happened to n?
1
0
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1,669
help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 15:04:36
$\frac{n^2}{n^4} = \frac{1}{n^2}$
0
1
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1,669
help-10
e267d99acbad4917963cf258e3459345
510,789,298,321,096,700
TeXit
11/11/2021 15:04:39
**reking**
https://cdn.discordapp.c…388548141059.png
123486388548141059.png
0
1
null
null
null
null
null
1,669
help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 15:05:27
$\frac{n \cdot n}{n \cdot n \cdot n \cdot n}$
0
1
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null
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1,669
help-10
e267d99acbad4917963cf258e3459345
510,789,298,321,096,700
TeXit
11/11/2021 15:05:30
**reking**
https://cdn.discordapp.c…388548141059.png
123486388548141059.png
0
1
null
null
null
null
null
1,669
help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 15:05:31
they cancel out, right?
0
1
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:05:45
yes I understand that
1
0
null
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:06:03
but the final answer is -6.75
1
0
456,226,577,798,135,800
Deleted User
0000
Deleted User
false
1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:06:14
https://cdn.discordapp.c…6360/unknown.png
unknown.png
1
0
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null
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:06:23
oops wrong one
1
0
null
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:06:39
https://cdn.discordapp.c…2580/unknown.png
unknown.png
1
0
null
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null
null
null
1,669
help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 15:06:51
i guess i dont know what you mean by step 2 and step 3
0
1
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:06:54
I understand now how we go from step 1 to step 2
1
0
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:07:04
thanks for that
1
0
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null
1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:07:06
but now I am asking
1
0
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:07:19
how do we go from step 2, the middle line, to step 3
1
0
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:07:33
where n is no longer present and the solution is given as -6.75
1
0
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1,669
help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 15:07:51
because when n goes to infinity, you can simply remove all 1/n
0
1
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help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 15:07:57
it goes to zero
0
1
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help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 15:08:26
so you have $\frac{81}{4}(1+0)^2 - 27(1+0)^2$
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1,669
help-10
e267d99acbad4917963cf258e3459345
510,789,298,321,096,700
TeXit
11/11/2021 15:08:28
**reking**
https://cdn.discordapp.c…388548141059.png
123486388548141059.png
0
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:08:35
is that true for all variables when their limit is infinity?
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help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 15:08:54
yeah, well, theres nothing special about the l etter 'n'
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1,669
help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 15:09:03
if x goes to infinity, 1/x goes to zero
0
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:09:11
what about just x
1
0
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1,669
help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 15:09:16
that goes to infinity
0
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1,669
help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 15:09:20
so its troublesome
0
1
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1,669
help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:09:36
so if n where not 1/n in the above problem
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0
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:09:42
it would remain as n
1
0
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1,669
help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 15:09:51
thats why they did the stuff from top line to middle line. to get rid of n in the numerator
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:10:20
I see
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0
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:10:24
well thanks for the help
1
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:10:27
that has helped a lot
1
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:13:32
is there a place where I can find the limit laws?
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help-10
e267d99acbad4917963cf258e3459345
456,226,577,798,135,800
Deleted User
11/11/2021 15:13:43
so I know that as n approaches infinity that 1/n = 0
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help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 15:19:46
it can be shown like this. for any small $\epsilon > 0$, we can find a large $N$ such that the distance between 1/n and 0 $$|1/n - 0| = |1/n| $$ is less than $\epsilon$, whenever $n \geq N$
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help-10
e267d99acbad4917963cf258e3459345
510,789,298,321,096,700
TeXit
11/11/2021 15:19:49
**reking**
https://cdn.discordapp.c…388548141059.png
123486388548141059.png
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help-10
e267d99acbad4917963cf258e3459345
123,486,388,548,141,060
reking
11/11/2021 15:21:49
but if that doesn't make sense to you yet, i don't know how else to show it :v
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help-10
f1c771f25f974120b5ef14e281ef6ba7
399,727,937,634,566,140
Redacted
04/03/2022 18:54:44
I know that the given angle and the opposite one have to equal 90 degrees but I dont know how to do that in this form. I also dont really know what to do after that 😅 (plz ping)
https://cdn.discordapp.c…5866/unknown.png
unknown.png
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