As the title suggests the modification of this problem will be, that we will solve a more general series and then use a specific value to arrive at the solution of this problem.
First let us consider the following limit:
Observe carefully that using k=1 in this limit, we get the limit that has been asked to evaluate.
Now we can change the summand to an integral
(As the term is an ‘n’ free term)
So we see the solution is
Substituting k=1, we get