More fun in 2015, Part 16

Algebra Level 5

n=0Fn2015n\sum_{n=0}^{\infty}\frac{F_n}{2015^n} Find the sum above, where FnF_n is the Fibonacci sequence. Write the sum in the form ab\frac{a}{b}, where a>0a>0 and b>0b>0 are co-prime. Make aa your answer.

Note: F0=0,F1=1 F_0 = 0, F_1 = 1 .

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