Proving that Cauchy Summation converges

Asked May 22 '20 at 15:37

Active May 22 '20 at 15:37

Viewed 23 times

How can I prove that the following summation converges? $$\sum_{n=0}^\infty \sum_{k=0}^n \frac{(-1)^n}{(k+1)\times (n-k+1)}$$

I tried to prove that by proving that the following summation in in absolute value converges so the original one converges too, but that's incorrect.

Any other ideas?

Note: I found that if it converges then it converges to ln(2)^2 but that doesn't help since I want to prove the it converges at first place.

asked May 22 '20 at 15:37

Daniel98

1

I see you have now asked exactly the same question three times! Please stop doing this. I hope that some moderator will be able to merge the questions somehow. – Calum Gilhooley May 22 '20 at 16:07
A duplicate of [the OP's] Proving that $\sum_{n=0}^\infty \sum_{k=0}^n \frac{(-1)^n}{(k+1)\times (n-k+1)}$ converges – metamorphy May 22 '20 at 16:37

0 Answers0