Suppose I have the following finite alternating series:
$ \sum\limits_{k=1}^{n} (-1)^k \frac{a_k}{k} = 0$
Where $a_k > 0$ Can anything be said about the bounds of the series with a shifted denominator?:
$\sum\limits_{k=1}^{n} (-1)^k \frac{a_k}{k+1}$
Any help or pointers would be greatly appreciated!