Basic Analysis I — Real Analysis · Problem 2.6.1

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · series-convergence-divergence

Problem

Decide the convergence or divergence of the following series.

a)\; \sum_{n=1}^{\infty} \frac{1}{2^{2n+1}} \qquad b)\; \sum_{n=1}^{\infty} \frac{(-1)^n(n-1)}{n} \qquad c)\; \sum_{n=1}^{\infty} \frac{(-1)^n}{n^{1/10}} \qquad d)\; \sum_{n=1}^{\infty} \frac{n^n}{(n+1)^{2n}}