## Problem of the week

### 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.)