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3 dots meaning

Anonymous Fri 20 Nov 03:07:54 2020 No.12364591 View Reply Original Report

Quoted By: >>12364636 >>12364642 >>12364647 >>12364698

how does this work?

I have to investigate this for convergence and prove convergence,
but i don't even know how to read this
What the fuck is dot dot dot in that context?
i never seen this shit being written like this

does someone know how this works?

Anonymous

Anonymous Fri 20 Nov 2020 03:12:25 No.12364604 Report

Quoted By:

It means pattern repeating. 1, 2, 3,..., 6, 7, 8 is just 1 through 8. So 1,2, 3,..n is 1 through an arbitrary n

El Arcón

El Arcón Fri 20 Nov 2020 03:22:20 No.12364625 Report

Quoted By:

The numerator ends with an infinite string of pluses with an "n" at the like 0.999...8.

Anonymous

Anonymous Fri 20 Nov 2020 03:27:27 No.12364636 Report

Quoted By: >>12364660

>>12364591
Just weird factorial notation? Looks like it was written by a programmer.

Anonymous

Anonymous Fri 20 Nov 2020 03:31:13 No.12364642 Report

Quoted By:

>>12364591
It converges

Anonymous

Anonymous Fri 20 Nov 2020 03:32:16 No.12364647 Report

Quoted By:

>>12364591
=1

Anonymous

Anonymous Fri 20 Nov 2020 03:34:58 No.12364660 Report

Quoted By:

>>12364636
$a_n = \frac{n!}{(2n-1)!}$
Binomial theorem shit I think

Anonymous

Anonymous Fri 20 Nov 2020 03:37:43 No.12364670 Report

Quoted By: >>12364764

You guys are actually bald.
It's not factorial it's addition
Also op the last term is written in terms of n so you don't need to guess what the pattern is, from the form of the last term you can always tell

Anonymous

Anonymous Fri 20 Nov 2020 03:45:22 No.12364698 Report

Quoted By: >>12364713 >>12364727

>>12364591
It's a series, the n's after the . . . is the closed form
$\displaystyle \sum_{n=1}^\infty \frac{n}{2n-1}$

Anonymous

Anonymous Fri 20 Nov 2020 03:48:36 No.12364713 Report

Quoted By: >>12364733

>>12364698
its not a series, it is a sequence and it converges to one half. The numerator and denominator of the terms in the sequence are sums.

Anonymous

Anonymous Fri 20 Nov 2020 03:51:55 No.12364727 Report

Quoted By: >>12364740

>>12364698
This is wrong, it should be:
$a_n=\frac{\sum_{k=1}^nk}{\sum_{k=1}^n(2n-1)}$
Each individual a in the series doesn't run to infinity and the sum is within the numerator or the denominator respectively not outside the entire fraction

Anonymous

Anonymous Fri 20 Nov 2020 03:53:12 No.12364733 Report

Quoted By: >>12364736

>>12364713
Oh right I'm high, the numerator and denominator are series.

Anonymous

Anonymous Fri 20 Nov 2020 03:54:48 No.12364736 Report

Quoted By:

>>12364733
*sequence

Anonymous

Anonymous Fri 20 Nov 2020 03:56:48 No.12364740 Report

Quoted By:

>>12364727
Damn I said series instead of sequence too this thread is a trainwrexk

Anonymous

Anonymous Fri 20 Nov 2020 04:05:05 No.12364764 Report

Quoted By:

>>12364670
Lel right oops

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