Question

What is the sum of the infinite geometric series?

Answer 1

Answer: This series would have no last term. The general form of the infinite geometric series is a1+a1r+a1r2+a1r3+... , where a1 is the first term and r is the common ratio.

Explanation:

Answer 2

`S_(\infty)=(80)/(3)`

Explanation:

The sum of an infinite geometric series is given by:

`S_(\infty)=(a)/(1-r)`,

The given geometric series is

`\sum_(n=1)^(\infty)32(-(1)/(5))^(n-1)`

The constant ratio for this series is

`r=-(1)/(5)`

The first term of the series is
`a=32(-(1)/(5))^(1-1)=32`

The sum to infinity is
`S_(\infty)=(32)/(1--(1)/(5))`

`\implies S_(\infty)=(32)/((6)/(5))=(80)/(3)`