Question
A sequence $\{a_n\}$ of real numbers is said to be a Cauchy sequence of for each $\epsilon$ > 0 there exists a number $N > 0$ such that m, $n > N$ implies that $|a_n − a_m| <\epsilon$.
Prove that every convergent sequence is a Cauchy sequence
Attempt
This is my first time hearing what a cauchy sequence is. I have no idea how to even start this. I googled cauchy sequence and I think its when $a_n$ converges to $a_{n+1}$?
Attempt:
WTS: $\exists a_m \in \mathbb R, \forall \epsilon > 0, \exists N > 0$, such that for all $n \in \mathbb N$, if $n > N$, then $|a_n - a_m| < \epsilon$
Let $\epsilon > 0$ be arbitrary
Choose N such that for $n > N$ we have $|a_n - a_m| < \epsilon$
Suppose $n > N$, then
??
Could someone point me to the right direction? Thx.