Answer
The series diverges.
Work Step by Step
An infinite geometric series is a series of the form
$ a+ar+ar^{2}+ar^{3}+\cdots+ar^{n-1}+\cdots$
An infinite geometric series for which $|r| < 1$
has the sum $S=\displaystyle \frac{a}{1-r}$
If $|r| \geq 1$, the series diverges (the sum does not exist).
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$a=-1$
$ r=\displaystyle \frac{\frac{9}{8}}{-1}=-\frac{9}{8}, \quad$
Since $|r| \geq 1$, the series diverges.
