不如這樣看吧
let r=(4/9)
let s = 1 + 2r + 3r^2 + .... (1)
r*s = r + 2r^2 + .... (2)
(1) - (2):
(1-r)*s = 1 + r + r^2 + ... = 1/(1-r)
=> s = 1/(1-r)^2