Calculate Sum First N Natural Numbers in Java

Introduction

The sum of the first N natural numbers (1 + 2 + 3 + ... + N) is a common calculation in programming and mathematics. In Java, you can compute this sum using mathematical formulas or iterative approaches. This guide provides a complete solution with code examples and explanations.

Mathematical Formula

The sum of the first N natural numbers can be calculated using the formula:

This formula is derived from the observation that pairing numbers from the start and end of the sequence (1 + N, 2 + (N-1), etc.) each sum to N+1, and there are N/2 such pairs.

Example Calculation

For N = 5:

Sum = 5 × (5 + 1) / 2 = 5 × 6 / 2 = 15

Verification: 1 + 2 + 3 + 4 + 5 = 15

Java Implementation

There are several ways to implement this calculation in Java:

Using the Formula

public class SumCalculator {
    public static int sumFirstNNumbers(int n) {
        return n * (n + 1) / 2;
    }

    public static void main(String[] args) {
        int n = 10;
        int sum = sumFirstNNumbers(n);
        System.out.println("Sum of first " + n + " natural numbers: " + sum);
    }
}

Using Iteration

public class SumCalculator {
    public static int sumFirstNNumbers(int n) {
        int sum = 0;
        for (int i = 1; i <= n; i++) {
            sum += i;
        }
        return sum;
    }

    public static void main(String[] args) {
        int n = 10;
        int sum = sumFirstNNumbers(n);
        System.out.println("Sum of first " + n + " natural numbers: " + sum);
    }
}

Using Java Streams

import java.util.stream.IntStream;

public class SumCalculator {
    public static int sumFirstNNumbers(int n) {
        return IntStream.rangeClosed(1, n).sum();
    }

    public static void main(String[] args) {
        int n = 10;
        int sum = sumFirstNNumbers(n);
        System.out.println("Sum of first " + n + " natural numbers: " + sum);
    }
}

Worked Examples

Example 1: Sum of first 10 natural numbers

Using the formula:

Sum = 10 × (10 + 1) / 2 = 10 × 11 / 2 = 55

Verification: 1+2+3+4+5+6+7+8+9+10 = 55

Example 2: Sum of first 100 natural numbers

Using the formula:

Sum = 100 × (100 + 1) / 2 = 100 × 101 / 2 = 5050

Verification: The sum of numbers from 1 to 100 is indeed 5050.