We're asked to show the improper integral

as a power series.

I start with what I know. That is

So...

I'm trying to see the pattern here, in order to put this in sigma notation, however I'm afraid that when I do I still won't grasp what's going on here with series.

Knowing that, it's not hard to integrate the terms and see that

But here's where I get stuck...

Am I going about this the right way?

Thanks in advance.