Lebl-Basic-Analysis-I · Problem 2.4.8

Sequences and Series

Mathematics · cauchy-sequences

Problem

True or false, prove or find a counterexample: If {xn}n=1∞\{x_n\}_{n=1}^\infty is a Cauchy sequence, then there exists an MM such that for all n≥Mn \geq M, we have ∣xn+1−xn∣≤∣xn−xn−1∣|x_{n+1} - x_n| \leq |x_n - x_{n-1}|.

Related theory

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