Question

Write a class called MathProgressions which has a main method (NOPE! NO DRIVERS THIS WEEK), and two methods which will calculate the geometric and harmonic progressions via a recursive method.

The class MathProgressions needs to have the following:

• Make sure to import java.util.*;
• Static Methods
  • Main method which handles all of the input and output. The user is asked to enter a number and then for that number it gives both the geometric and harmonic progressions for every number up until (and including) that number.
  • geometric: Is a method which takes in a number and then returns that value of the number in the geometric sequence. The geometric sequence is represented by:

geometric(n) = n × 11

Which mean it?s the product of all of the numbers up until that number.

• harmonic: Is a method which takes a number and then returns the value of the number in the harmonic sequence. The harmonic sequence is represented by:

Which means the product of the inverse of the first n numbers.

• NOTE: MAKE SURE EACH OF THESE ARE SOLVED RECURSIVELY AND NOT WITH A LOOP OR ELSE -79 FOR YOU!!!
• NOTE: YOU MAY USE A LOOP TO PRINT OUT THE PROGRESSION BUT NOT FOR THE CALCULATION

Example Dialog:

Enter a number and I'll give you the geometric and harmonic sequences

10

Geometric is:

1=1.0 2=2.0 3=6.0 4=24.0 5=120.0 6=720.0 7=5040.0 8=40320.0 9=362880.0 10=3628800.0

Harmonic is:

1=1.0 2=0.5 3=0.16666666666666666 4=0.041666666666666664 5=0.008333333333333333 6=0.0013888888888888887 7=1.9841269841269839E-4 8=2.4801587301587298E-5 9=2.7557319223985884E-6 10=2.7557319223985883E-7

Answer 1

import java.util.Scanner;

public class Progression
{
  public static void main(String [] args)
  {
    Scanner keyboard = new Scanner (System.in);
    System.out.println(
      "This program will calculate the geometric and ");
    System.out.println(
      "harmonic progression for the number you enter.");
    System.out.print(
      "Enter an integer that is greater than or equal to 1:  ");                
        
    int input = keyboard.nextInt();
    int geomAnswer = geometricRecursive (input);
    double harmAnswer = harmonicRecursive (input);
                
    System.out.println("Using recursion:");
    System.out.println("The geometric progression of " + input + " is " + geomAnswer);
    System.out.println("The harmonic progression of " + input + " is " + harmAnswer);
                
    geomAnswer = geometricIterative (input);
        harmAnswer = harmonicIterative (input);
        
    System.out.println("Using iteration:");
    System.out.println("The geometric progression of " + input + " is " + geomAnswer);
        System.out.println("The harmonic progression of " + input + " is " + harmAnswer);
        }
        
        public static int geometricRecursive (int n)
        {
                if (n == 0)
                {
                        return 1;
                }
                else
                {
                        return (geometricRecursive(n-1) * n);
                }
        }
        
        public static int geometricIterative (int n)
        {
                int product = 1;
                for (int index = 1; index <= n; index++)
                {
                        product = product * index;
                }
                return product;
        }
        
        public static double harmonicRecursive (int n)
        {
                        if (n == 0)
                {
                        return 1;
                }
                else
                {
                        return (harmonicRecursive(n-1) / (double)n);
                }
        }
        
        public static double harmonicIterative (int n)
        {
                double product = 1;
                for (int index = 1; index <= n; index++)
                {
                        product = product /(double)index;
                }
                return product;
        }
        
}

Answer 2

import java.util.Scanner;

public class Progression
{
  public static void main(String [] args)
  {
    Scanner keyboard = new Scanner (System.in);
    System.out.println(
      "This program will calculate the geometric and ");
    System.out.println(
      "harmonic progression for the number you enter.");
    System.out.print(
      "Enter an integer that is greater than or equal to 1:  ");                
        
    int input = keyboard.nextInt();
    int geomAnswer = geometricRecursive (input);
    double harmAnswer = harmonicRecursive (input);
                
    System.out.println("Using recursion:");
    System.out.println("The geometric progression of " + input + " is " + geomAnswer);
    System.out.println("The harmonic progression of " + input + " is " + harmAnswer);
                
    geomAnswer = geometricIterative (input);
        harmAnswer = harmonicIterative (input);
        
    System.out.println("Using iteration:");
    System.out.println("The geometric progression of " + input + " is " + geomAnswer);
        System.out.println("The harmonic progression of " + input + " is " + harmAnswer);
        }
        
        public static int geometricRecursive (int n)
        {
                if (n == 0)
                {
                        return 1;
                }
                else
                {
                        return (geometricRecursive(n-1) * n);
                }
        }
        
        public static int geometricIterative (int n)
        {
                int product = 1;
                for (int index = 1; index <= n; index++)
                {
                        product = product * index;
                }
                return product;
        }
        
        public static double harmonicRecursive (int n)
        {
                        if (n == 0)
                {
                        return 1;
                }
                else
                {
                        return (harmonicRecursive(n-1) / (double)n);
                }
        }
        
        public static double harmonicIterative (int n)
        {
                double product = 1;
                for (int index = 1; index <= n; index++)
                {
                        product = product /(double)index;
                }
                return product;
        }
        
}