# 2016-11 Infinite series

For a positive integer $$n$$, define $$f(n)$$ by
$f(n) = \begin{cases} 0 & \text{ if } n \equiv 0 \pmod{5} \\ 1 & \text{ if } n \equiv \pm 1 \pmod{5} \\ -1 & \text{ if } n \equiv \pm 2 \pmod{5} \end{cases}.$
Compute the infinite series
$\sum_{n=1}^{\infty} \frac{f(n)}{n} = 1 – \frac{1}{2} – \frac{1}{3} + \frac{1}{4} + \frac{1}{6} – \dots.$

(This is the last problem of this semester. Thank you.)

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