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Homework Statement
Prove that
sigma[n=0,inf] ((-1)^n n)/(n+1)
diverges
Homework Equations
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