Java Program to Find the Sum of Natural Numbers

Introduction

The sum of natural numbers up to a given number ( n ) is a common mathematical problem. Natural numbers are positive integers starting from 1. The sum of the first ( n ) natural numbers can be calculated using either a loop or the formula ( \text{Sum} = \frac{n \times (n + 1)}{2} ). This guide will walk you through writing a Java program that calculates the sum of the first ( n ) natural numbers.

Problem Statement

Create a Java program that:

Prompts the user to enter a positive integer ( n ).
Calculates the sum of the first ( n ) natural numbers.
Displays the result.

Example:

Input: 5
Output: "The sum of the first 5 natural numbers is 15"
Input: 10
Output: "The sum of the first 10 natural numbers is 55"

Solution Steps

Read the Number: Use the Scanner class to take the number ( n ) as input from the user.
Calculate the Sum Using a Loop: Use a loop to sum up all numbers from 1 to ( n ).
Display the Result: Print the calculated sum.

Java Program Using a Loop

// Java Program to Find the Sum of Natural Numbers // Author: https://www.rameshfadatare.com/ import java.util.Scanner; public class SumOfNaturalNumbers { public static void main(String[] args) { // Step 1: Read the number from the user try (Scanner scanner = new Scanner(System.in)) { System.out.print("Enter a positive integer: "); int n = scanner.nextInt(); // Step 2: Calculate the sum of natural numbers using a loop int sum = 0; for (int i = 1; i <= n; i++) { sum += i; } // Step 3: Display the result System.out.println("The sum of the first " + n + " natural numbers is " + sum); } } }

Java Program Using the Formula

// Java Program to Find the Sum of Natural Numbers Using Formula // Author: https://www.rameshfadatare.com/ import java.util.Scanner; public class SumOfNaturalNumbersFormula { public static void main(String[] args) { // Step 1: Read the number from the user try (Scanner scanner = new Scanner(System.in)) { System.out.print("Enter a positive integer: "); int n = scanner.nextInt(); // Step 2: Calculate the sum using the formula int sum = n * (n + 1) / 2; // Step 3: Display the result System.out.println("The sum of the first " + n + " natural numbers is " + sum); } } }

Explanation

Step 1: Read the Number

The Scanner class is used to read an integer input from the user. The nextInt() method captures the input number ( n ).

Step 2: Calculate the Sum

Using a Loop: A for loop is used to iterate through numbers from 1 to ( n ), adding each number to a cumulative sum.
Using the Formula: The sum of the first ( n ) natural numbers is calculated using the formula ( \text{Sum} = \frac{n \times (n + 1)}{2} ).

Step 3: Display the Result

The program prints the calculated sum using System.out.println().

Output Example

Example 1: Using a Loop

Enter a positive integer: 5 The sum of the first 5 natural numbers is 15

Example 2: Using the Formula

Enter a positive integer: 10 The sum of the first 10 natural numbers is 55

Conclusion

These Java programs demonstrate how to calculate the sum of the first ( n ) natural numbers using both a loop and a mathematical formula. They cover essential concepts such as loops, arithmetic operations, and user input handling, making them valuable exercises for beginners learning Java programming.