The series is converges if there exist a finite limit of partial sum sequence and is the sum of the series .

If the limit isn't exist, we say that the series is divergent.

Now, to telescopic series.

is telescopic series.

Partial sum of is:

By the definition above converges if exist.

Hence, , so converges iff converges.

In your case:

is converges sequence, so the series is also converges.

and , hence