Saturday 26 March 2016

sequences and series - How do i evaluate this :$sum_{k=1}^{+infty}frac{{(-1)^k}}{sqrt{k+1}+sqrt{k}}$?

I have tried to evaluate the bellow sum using some standard altern sum but i don't succed then my question here is :





Question:

How do i evaluate this sum





$\sum_{k=1}^{+\infty}\frac{{(-1)^k}}{\sqrt{k+1}+\sqrt{k}}$ ?



Note: Wolfram alpha show it's values here

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