Basic Analysis I — Real Analysis · Problem 2.5.3

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{3}{9n+1} \qquad b)\; \sum_{n=1}^{\infty} \frac{1}{2n-1} \qquad c)\; \sum_{n=1}^{\infty} \frac{(-1)^n}{n^2} \qquad d)\; \sum_{n=1}^{\infty} \frac{1}{n(n+1)} \qquad e)\; \sum_{n=1}^{\infty} n e^{-n^2}