Chapter 9.2, Problem 99E

(a)

To determine

To prove: The expression $\frac{1}{a_{n+1}{a}_{n+3}}=\frac{1}{a_{n+1}{a}_{n+2}}-\frac{1}{a_{n+2}{a}_{n+3}}$ with the Fibonacci sequence, $a_{n+2}=a_n+a_{n+1}$, where $a_1=1,a_2=1$.

(b)

To determine

To prove: The expression ${\displaystyle \sum _{n=0}^{\infty }\frac{1}{a_{n+1}{a}_{n+3}}}=1$ with the Fibonacci sequence, $a_{n+2}=a_n+a_{n+1}$, where $a_1=1,a_2=1$.