Basic Analysis I — Real Analysis · Problem 2.1.19

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · sequences-and-limits

Problem

(Easy) Let

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

be a sequence and

x \in \mathbb{R}

such that there exists a

k \in \mathbb{N}

such that for all

n \geq k

x_n = x

. Prove that

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

converges to

x