Chapter 10.2, Problem 97E

a.

To determine

To write: The first ten terms of the sequence.

b.

To determine

To check: The sequence is bounded.

c.

To determine

To estimate: The ratio of the successive terms of the sequence $\phi =\underset{n\to \infty }{\lim }\frac{f_{n+1}}{f_n}$; Provide evidence that $\phi =\frac{\left(1+\sqrt{5}\right)}{2}$.

d.

To determine

To verify: The result $f_n=\frac{1}{\sqrt{5}}\left({\phi }^n-{\left(-1\right)}^n{\phi }^{-n}\right)$ by induction.