1. ## Cauchy sequence

Prove that every convergent sequence is a Cauchy sequence.

[SOLVED] I will post my result if anyone is curious.

Thanks

2. I would like to see your result

3. Suppose $a_{n}$ $\rightarrow$ $a$.

$\forall$ $\epsilon > 0$, $\exists N$ $: |a_{n} - a| < \epsilon/2$, $\forall$ $k> N$. Then,

$|a_{n} - a_{m}| = |a_{n} - a + a - a{m}|$

Which is, $< |a_{n} - a| + |a - a_{m}|$

Which is, $< \epsilon/2 + \epsilon/2 = \epsilon$ $\forall$ $n,m > N$.

I recently discovered how to overuse quantifiers