Answer
converges to $\dfrac{1}{1-\sin x}$
Work Step by Step
Formula to calculate the sum of a geometric series is:
$S=\dfrac{a}{1-r}$;
Here, $a=1$ and common ratio $r =\sin x$
$S=\dfrac{a}{1-r}=\dfrac{1}{1-\sin x}$
Hence, the given series converges to $\dfrac{1}{1-\sin x}$