Question

How do you find the sum of the infinite geometric series given `16+12+9+...`?

Answer 1

Sum of the infinite geometric series is `64`

Explanation:

Sum of the infinite geometric series converges to `(a_1)/(1-r)`, where `a_1` is the first term and `r` is the common ratio and `|r|<1`.

Here, we have `a_1=16` and `r=12/16=9/12=3/4` and `|r|<1`,

Hence, sum of the infinite geometric series is

`16/(1-3/4)=16/(1/4)=16xx4=64`