MathNet 2009-part-05 — 172 problems (EN–VI) Question 117

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 $\sum_{n=0}^{\infty} F_{n} / 10^{n}$.