C++ Program to Find Sum of Natural Numbers Using Recursion

Natural numbers are positive numbers starting from 1, such as 1, 2, 3, and so on. Here, we will take a positive number n as input and and then will find the sum of all natural numbers from 1 up to n using recursion using C++ program.

Example

Input:
n = 5
The sum of the first 5 natural numbers is:
1 + 2 + 3 + 4 + 5 = 15
Output: 15

Input:
n = 8
The sum of the first 8 natural numbers is:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36
Output: 36

Using Recursion to Calculate Sum

To calculate the sum of the first n natural numbers, we repeatedly add each number from n down to 1. We use recursion, which means the function calls itself with a smaller value each time until it reaches a base case, where it stops.

Below are the steps we took:

• First, we create a function called sumNatural() that takes an integer n as input.
• Next, we check if n is equal to 1 . If it is, we return 1 . This is our base case.
• If n is not 1, we return n plus the result of sumNatural(n - 1). This breaks the problem into smaller parts.
• Finally, the function continues to call itself until it reaches the base case, and the results are added one by one as it returns.

C++ Program to Find Sum of Natural Numbers using Recursion

Here's a complete C++ program where we calculate the sum of n natural numbers using recursion.

#include <iostream>
using namespace std;

// Recursive function to calculate sum of first n natural numbers
int sumNatural(int n) {
    if (n == 1)  // base case: when n is 1, return 1
        return 1;
    return n + sumNatural(n - 1);  // recursive call
}

int main() {
    int n = 9;
    int sum = sumNatural(n);  
    // print the result
    cout << "Recursive sum of first " << n <<
        " natural numbers: " << sum << endl;
    return 0;
}

Once you run the above program, you will get the following output, which shows the sum of the first 9 natural numbers calculated using recursion:

Recursive sum of first 9 natural numbers: 45

Time Complexity: O(n) because the function calls itself n times.

Space Complexity: O(n) because each recursive call adds a new frame to the call stack.

Conclusion

In this article, we saw how to find the sum of the first n natural numbers using recursion in C++. We created a function that calls itself by reducing the value of n step by step, until it reaches the base case. This method is simple to understand but uses more memory than a loop because of repeated function calls.