# Math Help - bounding proof question..

1. ## bounding proof question..

how to prove that:
every sequence which convergences has to be bounded

2. Originally Posted by transgalactic
how to prove that:
every sequence which convergences has to be bounded
A sequence $\{s_n\}$ converges means that there exists an $N$ and an $s$ such that for all $n>N$

$|s_n-s|<1$.

Hence for all $n>N$:

$
|s_n|-|s|\le |s_n-s| < 1
$

so $|s_n|<1+|s|$

Therefore

$|s_n|\le \max \left[\left(\max_{0

CB

3. thanks