HMMT 2009 F7

Let $F_{n}$ be the Fibonacci sequence, that is, $F_{0}=0, F_{1}=1$ , and $F_{n+2}=F_{n+1}+F_{n}$ . Compute $\sum_{n=0}^{\infty} F_{n} / 10^{n}$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{10}{89}

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