Geometric series

Sum of a sequence with constant ratio — and when it converges.

A geometric series multiplies by a constant ratio r each step.

Sum of n terms

Sₙ = a(1 − rⁿ)/(1 − r)

Infinite sum (|r|<1)

S = a/(1 − r)

Try it

1 + 1/2 + 1/4 + 1/8 + ...

a=1, r=1/2. S = 1/(1−1/2) = 2.