Chapter 12.1, Problem 88AYU

(a)

To determine

The first $11$ terms of the Fibonacci sequence $u_{n+2}=u_{n+1}+u_n$ where the $n^{th}$ term of the sequence is $u_n=\frac{{\left(1+\sqrt{5}\right)}^n-{\left(1-\sqrt{5}\right)}^n}{2^n\sqrt{5}}$ and $u_1=1,u_2=1$.

(b)

To determine

The first $10$ terms of the ratio $\frac{u_{n+1}}{u_n}$.

(c)

To determine

The number that a ratio $\frac{u_{n+1}}{u_n}$ approach as $n$ gets larger.

(d)

To determine

The first $10$ terms of the ratio $\frac{u_n}{u_n+1}$.

(e)

To determine

The number that a ratio $\frac{u_n}{u_{n+1}}$ approach as $n$ gets larger.