a) Use the formula found in Example 4 for fnthe nth

Chapter 11, Problem 41E

(choose chapter or problem)

a) Use the formula found in Example 4 for fn, the $n$th Fibonacci number, to show that $f n$ is the integer closest to

$\frac{1}{\sqrt{5}}\left(\frac{1+\sqrt{5}}{2}\right)^{n}$

b) Determine for which $\mathrm{n}$ fn is greater than

$\frac{1}{\sqrt{5}}\left(\frac{1+\sqrt{5}}{2}\right)^{n}$

and for which $n$ fn is less than

$\frac{1}{\sqrt{5}}\left(\frac{1+\sqrt{5}}{2}\right)^{n}$

Equation Transcription:

$\frac{1}{\sqrt{5}}{\left({\frac{1+\sqrt{5}}{2}}\right)}^{n}$

$n$

$fn$

Text Transcription:

1/square root 5(1+square root 5/2)^n

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