I have some examples for this problem in my notes, but do not have the whole method shown step by step, and can not figure it out.
Take as an example:$$ \sum_{n=1}^{\infty} n 3^{-n} $$
I only have in my notes written the result, which is that this series converges, and the sum is .75; but can't figure out how to calculate the formula for partial sums, which I then calculate the limit of.