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June 22nd, 2017, 04:50 AM  #11 
Member Joined: May 2017 From: France Posts: 57 Thanks: 1 
Hi, $\displaystyle \text{The series is it converged } \sum\limits_{k=0}^n \frac{1}{\sqrt{k}}\cos(\frac{k^2+1}{k1}) \text{ ?}$ 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  
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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