Prove F(adsbygoogle = window.adsbygoogle || []).push({}); _{n}≤ (7/4)^{n}for all n, 0≤n

F_{n}= F_{n-1}+ F_{n-2}

Let P(n) be true for some n = k, for 0≤k

Let n = k+1

F_{k+1}≤ (7/4)^{k+1}

LHS: F_{k+1}= F_{k}+ F_{k-1}≤ F_{k-1}+ (7/4)^{k}≤ (7/4)^{k-1}+ (7/4)^{k}

This last line is where I'm stuck, I feel like either I messed up early on, or I'm missing a way of simplifying this to look like (7/4)^{k+1}

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# Fibonacci Sequence - Induction.

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