My Math Forum Convergent series : cos(k^2)/k

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 June 22nd, 2017, 04:50 AM #11 Member   Joined: May 2017 From: France Posts: 57 Thanks: 1 Hi, $\displaystyle \text{The series is it converged } \sum\limits_{k=0}^n \frac{1}{\sqrt{k}}\cos(\frac{k^2+1}{k-1}) \text{ ?}$ Cordially.
 June 24th, 2017, 03:21 PM #12 Newbie   Joined: Dec 2016 From: Austin Posts: 11 Thanks: 1 Question Can you verify the summation begins at 0? This would cause you to cross a singularity at k = 1, which would be an odd question. If the initial index of the summation is another number, please post the updated question. Thanks!
June 25th, 2017, 02:25 AM   #13
Member

Joined: May 2017
From: France

Posts: 57
Thanks: 1

Hi,

ERRATUM

Quote:
 Originally Posted by Dattier $\displaystyle \text{The series is it converged } \sum\limits_{k=2}^n \frac{1}{\sqrt{k}}\cos(\frac{k^2+1}{k-1}) \text{ ?}$
Cordially.

 June 27th, 2017, 05:37 AM #14 Senior Member   Joined: Mar 2015 From: New Jersey Posts: 1,390 Thanks: 100 These are Fourier series of f(x) evaluated for a particular value of x, which converge. That's not a proof- it's a direction of attack- a point of view.
 June 27th, 2017, 05:55 AM #15 Member   Joined: May 2017 From: France Posts: 57 Thanks: 1 Maybe

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