Bulletin Boards

Problem of the week

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.)