Finding a Closed Form from a Power Series

[Frillth]

Homework Statement

I have f(x) = the series x^k/[(k-1)k] summed from x=2 to infinity, and I need to find its closed form. Hint: What is the derivative of f(x)

Homework Equations

None.

The Attempt at a Solution

To start this problem, I took the derivative of the series, which makes the general term x^(k-1)/(k-1), which is x + x^2/2 + x^3/3... How do I get a function from this? I know this series looks really familiar, but I can't seem to remember where I've seen it before.

 

[StatusX]

Take the derivative one more time.