Basic Analysis I — Real Analysis · Problem 2.5.7

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · series-convergence

Problem

(Challenging): Suppose

\{x_n\}_{n=1}^{\infty}

is a decreasing sequence and

\sum_{n=1}^{\infty} x_n

converges. Prove

\lim_{n \to \infty} n x_n = 0