Basic Analysis I — Real Analysis · Problem 2.5.14

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · series-convergence

Problem

Suppose

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

converges and

x_n \geq 0

for all

n

. Prove that

\sum_{n=1}^{\infty} x_n^2

converges.