The convergence of the series $\sum (-1)^n \frac{n}{n+1}$ and the value of its sum This sum seems convergent, but how to find its precise  value? 
$$\sum\limits_{n=1}^{\infty}{(-1)^{n+1} \frac{n}{n+1}} = \frac{1}{2}-\frac{2}{3}+\frac{3}{4}-\frac{4}{5}+...=-0.3068... $$ Any help would be much appreciated. 

Hint: This series can't converge, since |$a_n| \rightarrow 0$ is not true, because $\frac{n}{n+1}=1$, if $n \rightarrow \infty$(This is a neccessary term).
