Infinite geometric sum (asking for insight on an easier solution) – math.stackexchange.com

Let the sequence $F$ be defined as: $F_1=F_2=1$ and $F_n=2F_{n-1}+F_{n-2}$, for $n>2$. Evaluate $\sum_{n=1}^{\infty}\frac{F_n}{10^n}$. The obvious solution involves solving for the explicit ...

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