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 $\displaystyle \{s_n\}$ converges means that there exists an $\displaystyle N$ and an $\displaystyle s$ such that for all $\displaystyle n>N$

$\displaystyle |s_n-s|<1$.

Hence for all $\displaystyle n>N$:

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

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

Therefore

$\displaystyle |s_n|\le \max \left[\left(\max_{0<k<N-1}|s_k|\right),1+|s|\right]$

CB

3. thanks