Solving an equation using transformation

Solve where . I'm not exactly sure of how to do it, but I guess it's easier to comment if I show how I'd like to solve it. What I really need help with are the summations, and how to alter the starting integer while rewriting the sums. I tried to get every step on the way here, that's why the post is bloated. (Wait)

I start out with

- I seem to remember adding one, n = 1, when differentiate... Please comment!

- This is one thing I'm unsure of. should it be n = 2 in the summation? Please comment!

Back to the equation.

In the first series use n = k + 1

- Once again I'm unsure of the starting integer of the sum. Is it right to subtract one when I use n = k + 1?