Question 49
Compute the sum
$$
\sum_{n=1}^{\infty} \frac{F_n}{10^{n+1}}
$$
where $F_n$ is the $n$th Fibonacci number given by $F_1 = F_2 = 1$ and $F_{n+1} = F_n + F_{n-1}$ for all $n \geq 2$.
$$
\sum_{n=1}^{\infty} \frac{F_n}{10^{n+1}}
$$
where $F_n$ is the $n$th Fibonacci number given by $F_1 = F_2 = 1$ and $F_{n+1} = F_n + F_{n-1}$ for all $n \geq 2$.