Complex Analysis: Theory and Applications · Problem 4.1.10

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · series-convergence-divergence

Problem

State (with justification) whether the following series converge. (a)

\displaystyle\sum_{n=1}^{\infty} \frac{i^n}{n}

. (b)

\displaystyle\sum_{n=1}^{\infty}\left(\frac{1}{n} + \frac{i}{2^n}\right)