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Mathematically, computing the sum S = Sigma^n_i=1 1/i(I + 1) as A = 1/1(1 + 1) +

ID: 3663587 • Letter: M

Question


Mathematically, computing the sum S = Sigma^n_i=1 1/i(I + 1) as A = 1/1(1 + 1) + 1/2(2 + 1) + ...+ 1/n(n + 1) should be equal to computing it as B = 1/n(n + 1) +...+ 1/2(2 + 1) + 1/1(1 + 1). Additionally, note that the closed form of this sum is S = n/n + 1. Write a computer program to take an input variable n, evaluate A and B (with the sum computed in the order from left to right as shown above), and compute the absolute errors S - A and S - B using the closed form of S. Run your program 6 times to provide input values of n of 10, 50, 100, 500, 1000, and 5000, and tabulate and analyze your results. Please include your source code in addition to your tabulated and analyzed results in your homework.

Explanation / Answer

Answer:

import java.util.*;
class Ordercode
{
   public static void main(String args[])
   {
       int i;
       int z=0;
       int temp=0;
       int y=0;
       Scanner in = new Scanner(System.in);
       double k=0.0;
       double calc=0;
       double s=0.0;
       //int n=10;
       System.out.println("Enter value of n:");
       int n = in.nextInt();
       System.out.println("You entered integer "+n);
       double m=0.0;
       for(i=1;i<=n;i++)
       {
           z=i*(i+1);
          
           //System.out.println(z);
           k=1/(double)z;
           //System.out.println(k);
           y=z*4;
           //System.out.println(y);
           calc=10/(double)y;
          
          
           m=n/(double)(n+1);
          
          
          
       }
       System.out.println("calc is "+calc);
       System.out.println("m is "+m);
       double finalcalc=m-calc;
       System.out.println("final calc is"+finalcalc);
       //System.out.println(k);
       //System.out.println(n);
   }
}