(Solved) : Exercise Show Using Strong Induction Let B Show C Assume K 3 4 N Show Hint Use Result F Q29918249 . . . .

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In this exercise we show, using strong induction, that when $>24 (1)$ where $f_{n}= f_{n-1} + f_{n-2}$ with $f_{0}=0$ and $f_{1}=1$ .

a) Let $delta =$ $frac{1+sqrt{5}}{2}, x^{2} = (x+1)$

b) Show that $f_{3}> delta$

c) Now assume that $f_{k} > delta ^{k-2}$ for all k ? {3, 4, …, n}, and show that $f_{n+1}> delta ^{n+1-2}$ . Hint use the result of a) FYI: $f_{n}$ and $delta$ are known by the Fibonacci sequence and the Golden Ratio.

>24 (1) Show transcribed image text

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(Solved) : Exercise Show Using Strong Induction Let B Show C Assume K 3 4 N Show Hint Use Result F Q29918249 . . . .

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