MHB What is the connection between the natural logarithm and the limit of a series?

[brunette15]

I am attempting to solve the limit for the following series:
-1 + 1/2 - 1/3 + 1/4 ... (-1)^n/(n+1)

I am able to determine that the series converges by applying the ratio test however i am having trouble evaluating the limit itself :/

 

[Nono713]

I would suggest taking a look at the Taylor expansion of the natural logarithm at $x = 1$. You should notice a similarity with your series.