Example: Sum of Series (Geometric Formula) in C++

// Sum of Series (Geometric Formula)
#include <iostream>
#include <cmath>    // For std::pow
#include <iomanip>  // For std::fixed and std::setprecision
using namespace std;

int main() {
    // Step 1: Declare variables for x, n, and sum
    double x;
    int n;
    double sum = 0.0;

    // Step 2: Prompt user for input
    cout << "Enter the value of x: ";
    cin >> x;
    cout << "Enter the number of terms (n): ";
    cin >> n;

    // Step 3: Input validation
    if (n <= 0) {
        cout << "Number of terms (n) must be positive." << endl;
        return 1;
    }

    // Step 4: Apply the geometric series formula
    if (x == 1.0) {
        // If x is 1, each term is 1, so sum is n * 1
        sum = n;
    } else {
        // Use the formula: S = (x^n - 1) / (x - 1)
        sum = (pow(x, n) - 1.0) / (x - 1.0);
    }

    // Step 5: Display the result
    cout << fixed << setprecision(6); // Set precision for output
    cout << "Sum of the series for x = " << x << " and n = " << n << " is: " << sum << endl;

    return 0;
}