Fibonacci in Decimal
Let $F_1 = F_2 = 1$ and $F_{n+1} = F_n + F_{n-1}$. Find the exact value of $\sum_{n=1}^{\infty} F_n / 10^n = 0.1 + 0.01 + 0.002 + 0.0003 + 0.00005 + \dots$. Give your answer as a reduced fraction.
Related problems & prerequisites
Worth solving first
- Dominoes and Big Squares 4.0/10
- Tiling with Dominoes 3.9/10
- No Consecutive Elements 3.5/10
Source: Classic generating-function exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.