how to simplify this please?

Let x be P+P*R+P*R^2+P*R^3+...+ P*R^n

x = P+P*R+P*R^2+P*R^3+...+ P*R^n - (1)
x*R = P*R + P*R^2 + P*R^3 + P*R^n + P*R^(n+1) - (2)

(2) - (1)
x*R - x = P * R^(n+1) - P
x(R-1) = P[R^(n+1) - 1]
x = P[R^(n+1) - 1] / (R-1)

∴P+P*R+P*R^2+P*R^3+...+ P*R^n = P[R^(n+1) - 1] / (R-1)

here is the solution:

圖片參考：http://img511.imageshack.us/img511/8785/dfhfhxv5.jpg

P+PxR+PxR^2+PxR^3+...+ PxR^n = PxR^(n-1)