I am trying to derive the formula for the variance of a geometric distribution and am stuck at the following problem:
I need to find the sum to infinity for the following series:
$1+3(1-p)+5(1-p)^2+7(1-p)^3+\dots$ where $p$ where $p$ is a constant $0<p<1$
The series looks like the sum of the odd numbers and the sum of a geometric series (with common ration $(1-p)$) combined.
I don't know how to deal with such series. Please tell me how to solve this.