More fun in 2015, Part 16

Algebra Level 4

\[\sum_{n=0}^{\infty}\frac{F_n}{2015^n}\] Find the sum above, where \(F_n\) is the Fibonacci sequence. Write the sum in the form \(\frac{a}{b}\), where \(a>0\) and \(b>0\) are co-prime. Make \(a\) your answer.

Note: \( F_0 = 0, F_1 = 1 \).

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