Infinite Fibonacci Fractions

Algebra Level 3
  1. Let a/b (where both a and b are positive integers ) equal 1/5+1/25+2/125+...+F(n)/5^n, where F(n) is the nth Fibonacci number, defined by F(1) = F(2) = 1 and F(n)= F(n-1) + F(n-2) for all integers n>2. Find 10a+b.
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