(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that

sigma[n=0,inf] ((-1)^n n)/(n+1)

diverges

2. Relevant equations

3. The attempt at a solution

I'm unsure how to do this

I tried applying the alternating sereis test but when I did so I got

(n/(n+1))' = 1/(n+1)^2

so I can't say that the terms are non increasing and so the conditions are not meant for the alternating series test

I tried applying the root test and got an infinite loop of l hospital's rule (or however it's spelled) because of the square root so I couldn't come up with a conclusion based on that

I tried applying the ratio test and got r = 1 so the test was inconclusive

I don't know how to integrate something like ((-1)^n n)/(n+1)

so I concluded that the integral test was not going to work

Can I just simply say by the divergence test

lim n->inf ((-1)^n n)/(n+1) =/= 0

I'm having a hard time justifying that this is a true statement though...

I'm not experienced with applying comparison tests to alternating series...

thanks for any help

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# Calculus II - Infinite Series

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