Determine whether the series converges or diverges. If it is convergent, find the sum.

Question

Determine whether the series converges or diverges. If it is convergent, find the sum.

4 + 1 + 1/4 + 1/16 + ...

Answer 1

The initial term is 4 (lets call it a₁) and each succeeding term is multiplied by 1/4 so this series falls into the category of an infinite geometric series where the absolute value of the multiplier (lets call it "r") is < 1. Consequently, the series converges and it converges to a sum using the equation:

S = a₁/(1 - r)

S = 4/(1 - 1/4)

S = 4/(3/4)

S = 4•4/3

S = 16/3