`8+6+9/2+27/8+...` Find the sum of the convergent series.

`8+6+9/2+27/8+........`

Let's find the common ratio of the terms:

`r=a_2/a_1=6/8=3/4`

`r=a_3/a_2=(9/2)/6=9/12=3/4`

So this is a geometric sequence with common ratio of `3/4`

`S_oo=a/(1-r)`  where a is the first term

`S=8/(1-3/4)`

`S=8/(1/4)`

`S=32`

The sum of the given convergent series is 32.

`8+6+9/2+27/8+........`

Let's find the common ratio of the terms:

`r=a_2/a_1=6/8=3/4`

`r=a_3/a_2=(9/2)/6=9/12=3/4`

So this is a geometric sequence with common ratio of `3/4`

`S_oo=a/(1-r)`  where a is the first term

`S=8/(1-3/4)`

`S=8/(1/4)`

`S=32`

The sum of the given convergent series is 32.