ANSWER
Converges
[tex]S_{ \infty } = 68[/tex]
EXPLANATION
The guy sequence is
17 + 12.75 + 9.5625 + ...
The common ratio is:
[tex] \frac{9.5625}{12.75} = \frac{12.75}{17} = \frac{3}{4} = r[/tex]
Since
[tex] |r| < 1[/tex]
the series converges.
The sum to infinity of this sequence is :
[tex]S_{ \infty } = \frac{a}{1 - r} [/tex]
where a=17 is the first term of the series.
[tex]S_{ \infty } = \frac{17}{1 - \frac{3}{4} } [/tex]
[tex]S_{ \infty } = \frac{17}{ \frac{1}{4} } = 68[/tex]
