>>11129164S_n = a + a*r^1 + ... + a*r^(n-1) + a*r^n
r*S_n = a*r + a*r^2 + ... + a*r^n + a*r^(n+1)
r*S_n = S_n - a + a*r^(n+1)
r*S_n - S_n = -a + a*r^(n+1)
S_n(r-1) = -a + a*r^(n+1)
S_n = (-a + a*r^(n+1)) / (r-1)
take the limit as n goes to infinity (assuming |r| < 1). Because this is a infinite sum and has infinitely many terms.
