For the summation part:
You can shift the index, but you don't have to. The summand is 0 when n=0, so you can shift the index by 1 to get rid of adding 0.
If you are unsure, just check if the summand is 0 for the indices you are throwing away.
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.
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?