Basic Analysis I — Real Analysis · Problem 2.3.18

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · limit-superior-limit-inferior

Problem

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

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