kxk Summations

Dave's Math Tables: Geometric Summations

(Math | Calculus | Expansions | Geometric)

Summation Expansion Equivalent Value Comments

n
sum k x ^k
k=1 = 1 x¹ + 2 x² + 3 x³ + 4 x⁴ + ... = x / (x - 1)²

inf
sum r ^k
k=1 = 1 + r + r ² + r ³ + ... = 1 / (1 - r) Infinite Geometric Series (r not equal to 1)

Summation	Expansion	Equivalent Value	Comments
n k x ^k k=1	= 1 x¹ + 2 x² + 3 x³ + 4 x⁴ + ...	= x / (x - 1)²
r ^k k=1	= 1 + r + r ² + r ³ + ...	= 1 / (1 - r)	Infinite Geometric Series (r 1)