How can I find $$\sum_{n = 0}^{ \infty} \frac{F_n}{3^n}$$ If I know that the generating function for the Fibonacci sequence is $G(t) = \frac{t}{1 - t - t^2}$?
2026-03-27 22:04:47.1774649087
How to find $\sum_{n = 0}^{ \infty} \frac{F_n}{3^n}$
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Note that $$ \sum_{n=0}^\infty \frac{F_n}{3^n}t^n = \sum_{n=0}^\infty F_n\left(\frac{t}{3}\right)^n = G(t/3) $$