# 2016-12 A series

Let $$k$$ be a positive integer. Let $$a_n=1$$ if $$n$$ is not a multiple of $$k+1$$, and $$a_n=-k$$ if $$n$$ is a multiple of $$k+1$$. Compute $\sum_{n=1}^\infty \frac{a_n}{n}.$

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