Question

Write a C++ program to Calculate the value of π from the infinite series Print a table that shows the value of π approximated by computing the first 200,000 terms of this series. How many terms do you have to use before you first get a value that begins with 3.14159?

Answer 1

The C++ program is an illustration of loops and conditional statements

How to analyze the infinite series

The infinite series is given as:

$\pi = 4 - \frac 43 + \frac 45 - \frac 47 + \frac 49 -\frac 4{11} + ....$

The above series shows that, the addition and the subtraction signs are interchanged, and the denominator of the fractions increase by 2 while the numerator remains the same

The main program

The program written in C++, where comments are used to explain each line is as follows:

#include <iostream>

using namespace std;

int main(){

   //This initializes the value of pi to 0

   double pi = 0;

   //This iterates from 1 to 200000

   for(int i = 0; i< 200000; i++){

       //The following conditions determine the value of pi

       if(i%2==0){

           pi+=4.0/(1.0+2.0*i);

       }

       else{

           pi-=4.0/(1.0+2.0*i);

       }

   }

   //This prints the value of pi

   cout<<pi;

   return 0;

}

Read more about loops and conditional statements at:

brainly.com/question/24833629