357.A Fibonacci Telescope

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combinatoricsCh. 1 — Classical Probability and Combinatorics444+ Problems in Probability

Let

F_n

be the

n

th Fibonacci number (

F_1 = F_2 = 1

). Compute

\frac{F_1 + F_2 + F_3 + \cdots + F_{300}}{F_3 + F_6 + F_9 + \cdots + F_{300}}.

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