Question

Sum n=3 ^ infty 6 ( 2 3 )^ n-3

Answer 1

We need to evaluate this:

Let me attach the work:

You can see that the series is infinite geometric series.

The first term (a) would be:

`(2)/(3)^3=(8)/(27)`

The common ratio r is 2/3

So, sum to inifnity would be:

`\text{Sum}=(a)/(1-r)=((8)/(27))/(1-(2)/(3))=(8)/(9)`

Therefore:

`(81*((8)/(9)))/(4)`
`=18`

Answer is 18