You are right
When you sum, all the terms vanish except the two first ones
I've attached the problem I'm working on. I know how to do geometric series problems, but don't know how to attack this type of infinite series, and can't really make sense out of what my book tells me to do. I know it involves partial fractions somehow I just don't know what to do exactly.
Could someone help me out or at least clue me in on the procedure?
You can find something close to your problem here
You want to first do partial fractions:
Multiplying through by gives you
Since this is an identity, solve for and :
Hence and .
Now you know that
Now we have the sum
Let's write out the first several terms:
The rest of the solution is below, if you need it.