Thread: infinite sums

I was just musing about all the stuff I've forgotten because of a lack of use, and series came to mind. It's been years since I've studied or have had a use for them, but just for fun I was wanting to resharpen my skills. Take the following for example.

The most I can do with this one is test that it converges. Is it possible to solve it by hand, or are the only convergent series you can solve geometric?