Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE.

Question

sum from 1 to infinity of 1/e^2n.
It is convergent, but I do not know how to solve for the sum.

Answer 1

sure you do. It's just a geometric series

a = 1/e^2
r = 1/e^2

S = a/1-r = (1/e^2)/(1 - 1/e^2) = 1/(e^2-1)