Math2.org Math Tables: Geometric Summations

(Math)
SummationExpansionConvergenceComments
 n-1
sum r n
n=0		 = 1 + r + r 2 + r 3 + .. + r n-1
(first n terms)		 for r not equals 1,
= ( 1 - r n ) / (1 - r)
for r = 1,
= nr		 Finite Geometric Series
sum (n=0..inf) r n = 1 + r + r 2 + r 3 + ... for |r| < 1, converges to
1 / (1 - r)
for |r| >= 1
diverges 		Infinite Geometric Series

See also the Geometric Series Convergence in the Convergence Tests.