I'm trying to reduce the following nested summation (removing all summations), using the fact that: $\sum_{i=0}^\infty\ a^i = 1/(1- a)$.
Problem: $\sum_{n=0}^\infty\sum_{m=n}^\infty\ a^nb^m$
I know that if instead of m=n in the summation, we had m=0, it would be easy to reduce. I'd just use the above fact twice. How could I reduce this problem, removing all summations, using the above fact?
Note: Although this IS related to a homework assignment, you are welcome to post a final answer. This is just some algebra that's a part of a much larger probability question.