A lucky nest to call home ....

Algebra Level 4

$S = \displaystyle\sqrt{9 - \sqrt{\dfrac{13}{9} + \sqrt{\dfrac{13}{81} - \sqrt{\dfrac{13}{6561} + \sqrt{\dfrac{13}{43046721} - .......}}}}}$

If $S = \sqrt{\dfrac{a}{b}}$ where $a, b$ are both primes, find $a + b$ .