# Cauchy sequence

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• Dec 9th 2012, 10:22 PM
jackie
Cauchy sequence
Would someone help me with this problem?
Define the sequence $\{a_n\}$ in a metric space $(X,d)$ such that $d(a_{n+2},a_{n+1})\leq cd(a_{n+1},a_n)$ for $c\in (0,1)$. Show that $\{a_n\}$ is Cauchy.
• Dec 10th 2012, 01:47 AM
emakarov
Re: Cauchy sequence
See the proof of Banach fixed-point theorem.