Chapter 6.6, Problem 51E

The Binet form of Fibonacci numbers uses the formula

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

For example, to calculate F₈, substitute 8 for n in the previous formula. Using a calculator, due to roundoff errors, the author got 21.01904 for F₈, whose value is actually 21. Use this formula and a calculator to approximate the Fibonacci numbers in Exercises 51 –54 .

F₅