Chapter 13, Problem 13E

Consider the following sequence of equations involving Fibonacci numbers.

$1+2=31+2+5=81+2+5+13=211+2+5+13+34=55⋮$

a. Write down a reasonable choice for the fifth equation in this sequence.

b. Find the subscript that will make the following equation true.

$\text{F1}+\text{F3}+\text{F5}++\text{F21}=\text{F}$?

c. Find the subscript that will make the following equation true (assume N is odd).

$\text{F1}+\text{F3}+\text{F5}+\mathrm{...}\text{+FN}=\text{F}$?