Write the summation notation for the series and find the sum.

Question

1/5 + (1/5)^2 + (1/5)^3 + ... =

Answer 1

1/5 + (1/5)² + (1/5)³ + ... = ∑₁^∞(1/5)ⁿ = (1/5)/(1 - 1/5) = (1/5)/(4/5) = 1/4

We use formula for sum of infinite Geometric seciense: S_∞ = a₁/(1 - r)

Answer 2

∑(1/5)^k where the index k runs from 1 to ∞.

This is a geometric series and the sum is (1/5)/(4/5) = 1/4

The sum of an infinite geometric series is a/(1-r) where a is the first term and r is the ratio.