Chapter 1.2, Problem 24ES

Binet’s Formula Simplified Binet’s formula (see

Exercise 23) can be simplified if you round your calculator results to the nearest integer. In the following Formula, nint is an abbreviation for “the nearest integer of."

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

If you use $n=8$ in the above formula, a calculator will show 21.00951949 for the value inside the braces. Rounding this number to the nearest integer produces 21 as the eighth Fibonacci number.

Use the above form of Binet’s formula and a calculator to find the 16th, 21st, and 32nd Fibonacci numbers.