## Introduction

The sum of natural numbers is a common mathematical task that can be easily solved using a loop or a mathematical formula. Natural numbers are positive integers starting from 1. For example, the sum of the first 5 natural numbers (1 + 2 + 3 + 4 + 5) is 15. This guide will show you how to create a Java program that calculates the sum of the first n natural numbers.

## Problem Statement

Create a Java program that:

• Takes an integer input n from the user.
• Calculates and displays the sum of the first n natural numbers.

### Example 1:

• Input: n = 5
• Output: The sum of the first 5 natural numbers is 15

### Example 2:

• Input: n = 10
• Output: The sum of the first 10 natural numbers is 55

## Solution Steps

1. Prompt for Input: Use the Scanner class to read an integer input n from the user.
2. Calculate the Sum Using a Loop: Use a loop to add the numbers from 1 to n.
3. Display the Result: Print the calculated sum.
Mathematically, the sum of the first 'n' natural numbers can be found using a simple formula:

Sum=2n(n+1)

For example, if we want to find the sum of the first 5 natural numbers:

Sum=25(5+1)=15

## Java Program

### Approach 1: Using a for Loop

import java.util.Scanner;

/**
* Java Program to Find Sum of Natural Numbers using for loop
* Author: https://www.javaguides.net/
*/
public class SumOfNaturalNumbers {

public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);

// Step 1: Prompt the user for input
System.out.print("Enter a positive integer: ");
int n = scanner.nextInt();

// Step 2: Calculate the sum using a for 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);
}
}

### Explanation

• Input: The program prompts the user to enter a positive integer n.
• Sum Calculation: The program uses a for loop to iterate from 1 to n, adding each number to the variable sum.
• Output: The program prints the sum of the first n natural numbers.

### Output Example

#### Example 1:

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

#### Example 2:

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

### Approach 2: Using the Formula ( \text{Sum} = \frac{n(n + 1)}{2} )

import java.util.Scanner;

/**
* Java Program to Find Sum of Natural Numbers using Formula
* Author: https://www.javaguides.net/
*/
public class SumOfNaturalNumbersFormula {

public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);

// Step 1: Prompt the user for input
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

• Input: The program prompts the user to enter a positive integer n.
• Sum Calculation: The program calculates the sum using the formula ( \text{Sum} = \frac{n(n + 1)}{2} ), which provides a direct way to find the sum without looping.
• Output: The program prints the sum of the first n natural numbers.

### Output Example

#### Example 1:

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

#### Example 2:

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

## Conclusion

This Java program provides two methods to find the sum of the first n natural numbers: using a for loop and using a mathematical formula. Both methods are effective, but the formula method is more efficient because it calculates the sum in constant time without iteration. These methods are useful in various mathematical and computational tasks where the sum of natural numbers is required.