Please excuse my total ignorance but can someon explain to me how the following part of a certain proof makes sense(adsbygoogle = window.adsbygoogle || []).push({});

We want to show that Fk+1 ≤ (7/4)^(k+1). Consider fk+1 = fk + fk−1 (We can do this

as k +1 is at least 2; see the comment following the basis) < (7/4)^k +(7 /4)^(k−1) (by the Induction Hypothesis;

notice how the stronger hypothesis comes in handy here.)

The parts I bolded in red are mainly the things I dont understand. I plugged in the (7/4)...part into my calculator and did not get the alleged answer I was supposed to get if it were simply (7/4)^k+1. Can someone please enlighten me?

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# Component of Fibonacci Sequence

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