Harlan A. Brothers and John A. Knox discovered that as the value of x gets large

Question

Harlan A. Brothers and John A. Knox discovered that as the value of x gets larger, the value of the expression ( 2x+1/2x1 ) x gets closer and closer to e. Write a program that evaluates this expression for x = 1, 2, 3 and so on until he absolute difference between the expression’s value and the value of M E defined in math.h is less than 0.000001. Display he value if x that causes your loop to exit along with both the final approximation of e and the value of M E. Show seven decimal places. (in C with COMMENTS)

Explanation / Answer

Code :-

#include <stdio.h>
#include <math.h>

int main(void) {
   double x=0.0;
   double echeck=0.000001;
   const double e= 2.71828182845904524;
   double result;
   double diff;
   do{
        x++;
         result=(2*x + 1)/(2*x - 1); //expression
         if(result > e){    //conditions for absolute difference
               diff = result - e;
         }
        else{
            diff = e - result;
        }
   }while(diff < echeck);   //condition for checking whether the result is less than 0.000001

//printing all the values

   printf("The value of x = %2.0lf ",x);
   printf("The value of expression = %8.7lf ",result);
   printf("The value of e =%8.7lf ",e);
   return 0;
}

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