Basic Analysis I — Real Analysis · Problem 2.4.7

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · cauchy-sequences

Problem

Suppose {xn}n=1∞\{x_n\}_{n=1}^\infty is a Cauchy sequence such that for infinitely many nn, xn=cx_n = c. Using only the definition of Cauchy sequence prove that lim⁡n→∞xn=c\lim_{n\to\infty} x_n = c.

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