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Algebra Level 4

S=9139+1381136561+1343046721.......S = \displaystyle\sqrt{9 - \sqrt{\dfrac{13}{9} + \sqrt{\dfrac{13}{81} - \sqrt{\dfrac{13}{6561} + \sqrt{\dfrac{13}{43046721} - .......}}}}}

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

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