Chapter 6, Problem 14P

The value of p can be estimated from the expression:

$\frac{2}{\pi }=\frac{\sqrt{2}}{2}\cdot \frac{\sqrt{2+\sqrt{2}}}{2}\cdot \frac{\sqrt{2+\sqrt{2+\sqrt{2}}}}{2}\cdot \mathrm{...}$

Write a MATLAB program in a script file that determine p for any number of terms. The program asks the user to enter the number of terms, and then calculates the corresponding value of p. Execute the program with 5, 10, and 40 terms. Compare the result with pi. (Use format long.)