Question

How to Evaluate the equation in the picture, not sure what to do with the infinity

Answer 1

Recall that for an infinite geometric series of the form


`\displaystyle\sum_(n=0)^\infty ar^n`

as long as
`|r|<1`, the series converges to the value
`(a)/(1-r)`.

Here you have
`r=-\frac23`, so the series converges. You have


`\displaystyle\sum_(n=0)^\infty 5\left(-\frac23\right)^n=\frac5{1-\left(-\frac23\right)}=3`