Answer
The given series is convergent and its is 9.
Work Step by Step
The given series can be made into a similar form as the definition of the geometric series found in page 750 definition 4 -second line in the page- (by only factoring out a $3$ from the series and thus we will get: $3 * \Sigma (\frac{3}{4})^{n} $
Note that the summation of an infinite geometric series is $S= \frac{a}{1-r}$ if |$r$| $\lt 1 $ , here $r$ is the common ratio of the geometric series.
Now, If we choose n = 1 we can see that the initial term $a$ = $\frac{9}{4}$ and the common ratio $r$ = $\frac{3}{4}$ (Just by dividing any latter term by its former).
|$r$| = $\frac{3}{4}\lt 1 $, which means that the series is convergent.
Using: $S= \frac{a}{1-r}$ = $\frac{\frac{9}{4}}{1-\frac{3}{4}}$ = $\frac{\frac{9}{4}}{\frac{1}{4}}$ = 9.
The given series is convergent and its is 9.
