# Thread:

1. ## 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.

2. ## Re: Cauchy sequence

See the proof of Banach fixed-point theorem.
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