Basic Analysis I — Real Analysis · Problem 2.1.23

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · monotone-sequences

Problem

Suppose that {xn}n=1∞\{x_n\}_{n=1}^\infty is a monotone increasing sequence that has a convergent subsequence. Show that {xn}n=1∞\{x_n\}_{n=1}^\infty is convergent. Note: So Proposition 2.1.17 is an ``if and only if'' for monotone sequences.

Related theory

Browse the problem library