In this java program, we will learn about how to calculate the sum of natural numbers using recursion.

The natural numbers are the numbers that include all integers from 1 to infinity. To find the sum of all natural number till N, we have to add all numbers between 1 to N.

Let sumNumbers(N) be a method to calculate sum of natural numbers from 1 to N. Then

sumNumbers(N) = 1 + 2 + 3 + ... + N sumNumbers(N) = [1 + 2 + 3 + ... +(N-1)]+ N sumNumbers(N) = sumNumbers(N-1)+ N

From above recursion equation, to calculate natural number sum till N, we have to first calculate sum of natural numbers till (N-1) and then add N.

For Example:

sumNumbers(10) = sumNumbers(9) + 10

To understand this java program, you should have understanding of the following Java programming concepts:

## Java program to find the sum of natural numbers using recursion

public class NumbersSumRecursion { static int sumNumbers(int N) { if (N == 1) { return 1; } else { return sumNumbers(N - 1) + N; } } public static void main(String[] args) { int sum = sumNumbers(15); System.out.println("Sum of Numbers till 15 : "+sum); } }Output

Sum of Numbers till 15 : 120