Lebl-Basic-Analysis-I · Problem 2.3.18

Sequences and Series

Mathematics · limit-superior-limit-inferior-bolzano-weierstrass

Problem

Suppose {xn}n=1∞\{x_n\}_{n=1}^\infty is a sequence such that both lim inf⁡n→∞xn\displaystyle\liminf_{n\to\infty} x_n and lim sup⁡n→∞xn\displaystyle\limsup_{n\to\infty} x_n are finite. Prove that {xn}n=1∞\{x_n\}_{n=1}^\infty is bounded.

Related theory

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