Basic Analysis I — Real Analysis · Problem 2.1.13

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · monotone-sequences

Problem

Let {xn}n=1∞\{x_n\}_{n=1}^\infty be a convergent monotone sequence. Suppose there exists a k∈Nk \in \mathbb{N} such that lim⁡n→∞xn=xk.\lim_{n\to\infty} x_n = x_k. Show that xn=xkx_n = x_k for all n≥kn \geq k.

Related theory

Browse the problem library