Infinite series sum (1 Viewer)

omegadot · Apr 4, 2017

juantheron said:
$Evaluation of sum of series $\lim_{n\rightarrow \infty}\sum^{n}_{k=1}\frac{1}{(k-1)\sqrt{k}+k\sqrt{k+1}}$

$\noindent juantheron - Are you sure this infinite sum has a nice closed-formed solution? If$

$\sum^\infty_{k = 1} \frac{1}{(k + 1)\sqrt{k} + k \sqrt{k + 1}},$

$\noindent then the sum can be readily found by using some creative telescoping but I cannot see any way to find your sum. Am I missing something here?$

juantheron · May 6, 2017

my bad omegadot you are Right., I have got it, Thanks

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Infinite series sum (1 Viewer)

juantheron

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omegadot

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