Progression sums

Arithmetic progression sum

S(n, p) = sum(i**p for i in range(1, n)) = Theta(n ** (p + 1)), where p >= 1

Geometric progression sum

G(n, a) = sum(a ** i for i in range(1, n)) = a * (a ** (n+1) - 1) / (a - 1)

If n -> Infinity

G(n, a) = 1 / (1 - r)