geometric series with 13

Algebra Level pending

Find the sum of the following:

\[9+\frac{9}{13}+\frac{9}{13^{2}}+\frac{9}{13^{3}} +.....\]

The answer can be expressed as a top-heavy fraction \[\frac{x}{y}\] where x and y are co-prime.

x + y -2 is the 'n'th prime number

Work out the value of n

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