Basic Analysis I — Real Analysis · Problem 2.1.22

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · subsequences

Problem

Suppose that {xn}n=1∞\{x_n\}_{n=1}^\infty is a sequence such that the subsequences {x2n}n=1∞\{x_{2n}\}_{n=1}^\infty, {x2n−1}n=1∞\{x_{2n-1}\}_{n=1}^\infty, and {x3n}n=1∞\{x_{3n}\}_{n=1}^\infty all converge. Show that {xn}n=1∞\{x_n\}_{n=1}^\infty is convergent.

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