Lebl-Basic-Analysis-I · Problem 2.5.3

Sequences and Series

Mathematics · series-convergence-divergence

Problem

Decide the convergence or divergence of the following series. a)

\displaystyle\sum_{n=1}^{\infty} \frac{3}{9n+1}

\displaystyle\sum_{n=1}^{\infty} \frac{1}{2n-1}

\displaystyle\sum_{n=1}^{\infty} \frac{(-1)^n}{n^2}

\displaystyle\sum_{n=1}^{\infty} \frac{1}{n(n+1)}

\displaystyle\sum_{n=1}^{\infty} n e^{-n^2}