# ?How do you find the sum of the infinite geometric series 4 + 3.2 + 2.56 + 2.048 + …?

Jan 2, 2016

First find the common ratio (r) and make sure the series is convergent (0 ≤ r ≤ 1)

#### Explanation:

r = ${t}_{2} / {t}_{1}$

r = $\frac{3.2}{4}$

r = 0.8

S_∞ = $\frac{a}{1 - r}$

S_∞ = $\frac{4}{1 - 0.8}$

S_∞ = 20

The series has a sum of 20