Write a program to show how quickly the infinite sum below (an expression of Zen

Question

Write a program to show how quickly the infinite sum below (an expression of Zeno's paradox) converges to 1. The sum is expressed as follows: sigma_n = 1^infinity (where n = 1, 2, 3, ...) Prompt the user to enter the number of terms (between 10 and 25 inclusive) to be used in the approximation. Use a for loop to calculate each term in the sum and while doing so, to print a table. Each line of the table should include the term (value of n) number, the value of the term added to the sum at that iteration accurate to 6 decimal digits, and the value of the sum at that iteration also printed with 6 decimal digits. Use doubles for the term and sum approximation values.

Explanation / Answer

#include <iostream>
#include <iomanip>
using namespace std;

int main(){
cout << fixed << setprecision(6);
int n;
cout << "Enter the number of terms: ";
cin >> n;
double sum = 0, term = 1;
cout << "Iteration Term Sum ";
for(int i = 1; i <= n; i++){
term /= 2;
sum += term;
cout << i << " " << term << " " << sum << " ";
}
}

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