You can prove that the sum converges to 2 by considering the partial sums.
It turns out that (I encourage you to prove this):
Hence, taking the limit as n tends to infinity, you can see that the sum converges to 2.
I was wondering if there was any way to calculate the sum of the series
I know it is convergent by the ratio test, but it there anyway to finding out what sum it converges to?
This series came up when I was calculating the expected value of a random variable.
(Wolfram Alpha says it is 2, which makes sense in context of the problem)