I am struggling with solving sum of this alternate series:
$$ \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n(n+1)}\ $$
I know that:
$$ \log(1+x) = \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n} \cdot x^n\ $$
But It seems that I can't find a way to get to this form. Thanks.