Example of this theorem

see attached example it will help you if any doubt then ask

For an example, consider, (an) = 1 - 1/n, and (bn) = 2 - 1/n.

If you have any doubts, then ask

Hint : If an < bn, then bn - an > 0. Now consider, cn = bn - an. What can you say about cn? You can verify that, it's limit is b - a. Now you can proceed.