Math2.org Math Tables: Geometric Summations |
(Math) |
Summation | Expansion | Convergence | Comments |
n-1 r ^{n} n=0 |
= 1 + r + r ^{2} + r ^{3} + .. + r ^{n-1} (first n terms) |
for r 1, = for r = 1, = nr |
Finite Geometric Series |
r ^{n} | = 1 + r + r ^{2} + r ^{3} + ... | for |r| < 1, converges to 1 / for |r| >= 1 diverges |
Infinite Geometric Series |
See also the Geometric Series Convergence in the Convergence Tests.