Chapter 6, Problem 11P

The reciprocal Fibonacci constant $\psi$ is defined by the infinite sum:

$\psi ={\displaystyle \underset{n=1}{\overset{\infty }{\sum }}\frac{1}{F_n}}$

whereF_n, are the Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, .... Each element in this sequence of numbers is the sum of the previous two. Start by setting the first two elements equal to 1, then $F_n=F_{n-1}+F_{n-2}$ . Write a MATLAB program in a script file that calculates $\psi$ for a given n. Execute the program for n = 10, 50, and 100.