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June 22nd, 2017, 04:50 AM   #11
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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.
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June 24th, 2017, 03:21 PM   #12
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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!
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June 25th, 2017, 02:25 AM   #13
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Hi,

ERRATUM

Quote:
Originally Posted by Dattier View Post
$\displaystyle \text{The series is it converged } \sum\limits_{k=2}^n \frac{1}{\sqrt{k}}\cos(\frac{k^2+1}{k-1}) \text{ ?}$
Cordially.
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June 27th, 2017, 05:37 AM   #14
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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.
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June 27th, 2017, 05:55 AM   #15
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Maybe
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