Sum of N Natural Numbers

Lecture 15:- Sum of N Natural Numbers

The sum of the first N natural numbers is a common mathematical problem that can be solved using a formula or a loop in programming. The formula for finding the sum of the first N natural numbers is:

Sum = (N * (N + 1)) / 2

Here's an example Java program that calculates the sum of the first N natural numbers using a loop:

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import java.util.Scanner; public class SumOfNaturalNumbers {    public static void main(String[] args) {        Scanner scanner = new Scanner(System.in);        System.out.print("Enter the value of N: ");        int N = scanner.nextInt();        // Calculate the sum using a loop        int sum = 0;        for (int i = 1; i <= N; i++) {            sum += i;        }        System.out.println("Sum of the first " + N + " natural numbers is: " + sum);        scanner.close();    } }

Example output:

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Enter the value of N: 5 Sum of the first 5 natural numbers is: 15

In the program above, we use a for loop to iterate from 1 to N and keep adding each number to the sum variable. After the loop, we print the final sum.

However, it's worth noting that for large values of N, using the formula (N * (N + 1)) / 2 is more efficient than using a loop to add individual numbers. The formula has a time complexity of O(1), while the loop-based approach has a time complexity of O(N).