and define
Prove
Is it as simple as
Therefore,
you can rewrite this difference as the sum of two differences, and use a version of the triagle inequality.....
the "idea" behind this is that any convergent series is Cauchy, so for large enough n, two successive terms are as close as we like (this means something in terms of epsilon), so the "average" of the two successive terms (for large enough n) is going to be close to the limit as well.