Themes > Science > Mathematics > Calculus > Series Expansions >Geometric Summations
Summation Expansion Convergence Comments
 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


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