A ratio of Fibonacci sums

EasyBrainteasers~4m

Let $F_n$ be the $n$ -th Fibonacci number ( $F_1 = F_2 = 1$ ). Compute $\dfrac{F_1 + F_2 + F_3 + \dots + F_{300}}{F_3 + F_6 + F_9 + \dots + F_{300}}$ .

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$\sum_{k=1}^{n}F_k=F_{n+2}-1$ and $\sum_{j=1}^{m}F_{3j}=\tfrac{F_{3m+2}-1}{2}$ .
Both involve $F_{302}-1$ ; take the ratio.

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A ratio of Fibonacci sums

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