Given $\{a_n\}$ sequence which is bounded by: $m\le a_n \le M$ and converges to $L\in\mathbb{R}$. How do I prove that $m\le L \le M$?
Thank you very much.
Given $\{a_n\}$ sequence which is bounded by: $m\le a_n \le M$ and converges to $L\in\mathbb{R}$. How do I prove that $m\le L \le M$?
Thank you very much.
HINT: Suppose that $L>M$. Let $\epsilon=L-M$. Then there is an $n_0$ such that $L-\epsilon
You could also notice that $[m,M]$ is a closed set, and $a_n \in [m,M]$, for all $n$. Hence the limit must also be in $[m,M]$.