Question

Determine whether the geometric series 17 + 12.75 + 9.5625 + ... converges or diverges, and identify the sum if it exists.

Answer 1

Converges

`S_( \infty ) = 68`

Step-by-step explanation

The guy sequence is

17 + 12.75 + 9.5625 + ...

The common ratio is:

`(9.5625)/(12.75) = (12.75)/(17) = (3)/(4) = r`

Since

`|r| < 1`

the series converges.

The sum to infinity of this sequence is :

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

where a=17 is the first term of the series.

`S_( \infty ) = (17)/(1 - (3)/(4) )`

`S_( \infty ) = (17)/( (1)/(4) ) = 68`