Question

Find the sum of this infinite geometric series: 4 - 2.88 + 2.0736- 1.492992+...

Answer 1

Let
`r` be the common ratio between terms. Then


`-2.88=4r\implies r=-0.72`

Now denote the
`n`th partial sum of the series by


`S_n=4-2.88+2.0736-1.492992+\cdots+4(-0.72)^(n-1)+4(-0.72)^n`

Multiply both sides by
`-0.72`, then subtract from the above to get


`S_n-(-0.72S_n)=4-4(-0.72)^(n+1)`

`1.72S_n=4(1-(-0.72)^(n+1))`

`S_n=2.32558(1-(-0.72)^(n+1))`

As
`n\to\infty`, you're left with


`S_\infty=2.32558`