# Is it possible to write a sum as an integral to solve it?

I was wondering, for example,

Can:

Be written as an Integral? To solve it. I am NOT talking about a method for using tricks with integrals.

But actually writing an integral form. Like

What are some general tricks in finding infinite sum series.

A General Trick

A General Trick for summing this series is to use Telescoping Series:

An Integral Trick

Since

for $n\gt0$, we can write