Basic Analysis I — Real Analysis · Problem 2.4.4

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · cauchy-sequences

Problem

Let {xn}n=1∞\{x_n\}_{n=1}^\infty and {yn}n=1∞\{y_n\}_{n=1}^\infty be sequences such that lim⁡n→∞yn=0\lim_{n\to\infty} y_n = 0. Suppose that for all k∈Nk \in \mathbb{N} and for all m≥km \geq k, we have ∣xm−xk∣≤yk.|x_m - x_k| \leq y_k. Show that {xn}n=1∞\{x_n\}_{n=1}^\infty is Cauchy.

Related theory

Browse the problem library