Chapter 11.2, Problem 88E

(a)

To determine

To show:  The statement $\frac{1}{f_{n-1}{f}_{n+1}}=\frac{1}{f_{n-1}{f}_n}-\frac{1}{f_n{f}_{n+1}}$ is true.

(b)

To determine

To show:  The series ${\displaystyle \sum _{n=2}^{\infty }\frac{1}{f_{n-1}{f}_{n+1}}}=1$.

(c)

To determine

To show: The series ${\displaystyle \sum _{n=2}^{\infty }\frac{f_n}{f_{n-1}{f}_{n+1}}}=2$.