Chapter 11, Problem 2PP

A geometric progression is defined as the product of the first n integers and is denoted as

$\text{geometric}\left(n\right)={\displaystyle \underset{i=1}{\overset{n}{\prod }}i}$

where this notation means to multiply the integers from 1 to n. A harmonic progression is defined as the product of the inverses of the first n integers and is denoted as

$\text{geometric}\left(n\right)=\text{n}\times {\displaystyle \underset{i=1}{\overset{n-1}{\prod }}i}$

Both types of progression have an equivalent recursive definition:

$\text{geometric}\left(n\right)=n\times {\displaystyle \underset{i=1}{\overset{n-1}{\prod }}i}$

$\text{harmonic}\left(n\right)=\frac{1}{n}\times {\displaystyle \underset{i=1}{\overset{n-1}{\prod }}\frac{1}{i}}$

Write static methods that implement these recursive formulas to compute geometric(n) and harmonic(n). Do not forget to include a base case, which is not given in these formulas, but which you must determine. Place the methods in a test program that allows the user to compute both geometric(n) and harmonic(n) for an input integer n. Your program should allow the user to enter another value for n and repeat the calculation until signaling an end to the program. Neither of your methods should use a loop to multiply n numbers.