Shifting Denominator in a Finite Alternating Series

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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!