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C Program to Find the Sum of Natural Numbers using Recursion

In this C programming example, you will learn to find the sum of natural numbers using recursion.

C Program to Find the Sum of Natural Numbers using Recursion

In this example, you will learn to find the sum of natural numbers using a recursive function.

To understand this example, you should have the knowledge of the following C programming topics:

C User-defined functions

C Recursion

The positive numbers 1, 2, 3... are known as natural numbers. The program below takes a positive integer from the user and calculates the sum up to the given number.

Visit this page to find the sum of natural numbers using a loop.

Sum of Natural Numbers Using Recursion

#include

int addNumbers(int n);

int main() { int num;

printf("Enter a positive integer: ");

scanf("%d", &num);

printf("Sum = %d", addNumbers(num));

return 0; }

int addNumbers(int n) {

if (n != 0)

return n + addNumbers(n - 1);

else return n; } Run Code

Output

Enter a positive integer: 20

Sum = 210

Suppose the user entered 20.

Initially, addNumbers() is called from main() with 20 passed as an argument.

The number 20 is added to the result of addNumbers(19).

In the next function call from addNumbers() to addNumbers(), 19 is passed which is added to the result of addNumbers(18). This process continues until n is equal to 0.

When n is equal to 0, there is no recursive call. This returns the sum of integers ultimately to the main() function.

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Sum of natural numbers using recursion

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Sum of natural numbers using recursion

Difficulty Level : Easy

Last Updated : 16 Jun, 2022

Read Discuss(1) Courses Practice Video

Given a number n, find sum of first natural numbers. To calculate the sum, we will use a recursive function recur_sum().

Examples :

Input : 3 Output : 6

Explanation : 1 + 2 + 3 = 6

Input : 5 Output : 15

Explanation : 1 + 2 + 3 + 4 + 5 = 15

Recommended: Please try your approach on first, before moving on to the solution.

Below is code to find the sum of natural numbers up to n using recursion :

C++

// C++ program to find the

// sum of natural numbers up

// to n using recursion

#include

using namespace std;

// Returns sum of first

// n natural numbers

int recurSum(int n) { if (n <= 1) return n;

return n + recurSum(n - 1);

} // Driver code int main() { int n = 5;

cout << recurSum(n);

return 0; }

Java

Python

C#

PHP

Java Python C# PHP Javascript

Output :

15

Time complexity : O(n)Auxiliary space : O(n)

To solve this question , iterative approach is the best approach because it takes constant or O(1) auxiliary space and the time complexity will be same O(n).

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How to Find the Sum of Natural Numbers Using Recursion

Looking to better understand recursion? Learn how to find the sum of the first n natural numbers.

How to Find the Sum of Natural Numbers Using Recursion

By Yuvraj Chandra

Published Jun 22, 2021

Looking to better understand recursion? Learn how to find the sum of the first n natural numbers.

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Readers like you help support MUO. When you make a purchase using links on our site, we may earn an affiliate commission. Read More.

Recursion is a process in which a function calls itself directly or indirectly. Recursive algorithms are widely used in computer science to solve complex problems by breaking them down into simpler ones.

You can better understand recursive concepts by solving basic programming problems like the "product of two numbers", "the sum of first n natural numbers", and more.

In this article, you'll learn how to find the sum of the first n natural numbers using recursion.

Problem Statement

You're given a natural number n, you need to find the sum of the first n natural numbers using recursion.

Example 1: Let n = 5

Therefore, the sum of the first 5 natural numbers = 1 + 2 + 3 + 4 + 5 = 15.

Thus, the output is 15.

Example 2: Let n = 7

Therefore, the sum of the first 7 natural numbers = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28.

Thus, the output is 28.

Example 3: Let n = 6

Therefore, the sum of the first 6 natural numbers = 1 + 2 + 3 + 4 + 5 + 6 = 21.

Thus, the output is 21.

Recursive Function to Find the Sum of First N Natural Numbers

Most recursive functions have the following relative structure:

FUNCTION name IF condition THEN RETURN result ELSE CALL FUNCTION name END FUNCTION

To find the sum of the first n natural numbers, observe and apply the following pseudocode:

findSum(n): IF n<=1 THEN RETURN n ELSE

RETURN n + findSum(n-1)

END FUNCTION

Now, you can implement this pseudocode in your favorite programming language.

RELATED:

What Is A Function In Programming?

Note: You can also find the sum of the first n natural numbers using the following mathematical formula:

Sum of n natural numbers = n * (n + 1) / 2

Using this method you can find the sum in one step without using recursion.

C++ Implementation to Find the Sum of First N Natural Numbers Using Recursion

Below is the C++ implementation to find the sum of the first n natural numbers using recursion:

// C++ implementation to find the sum of

// first n natural numbers using recursion

#include

using namespace std;

// Recursive function to find the sum of first n natural numbers

int findSum(int n) { if (n<=1) { return n; } else {

return n + findSum(n-1);

} } // Driver code int main() {

int n1 = 5, n2 = 7, n3 = 6;

cout << "n1: " << n1 << endl;

cout << "n2: " << n2 << endl;

cout << "n3: " << n3 << endl;

cout << "Sum of first " << n1 << " natural numbers: " << findSum(n1) << endl;

cout << "Sum of first " << n2 << " natural numbers: " << findSum(n2) << endl;

cout << "Sum of first " << n3 << " natural numbers: " << findSum(n3) << endl;

return 0; } Output: n1: 5 n2: 7 n3: 6

Sum of first 5 natural numbers: 15

Sum of first 7 natural numbers: 28

Sum of first 6 natural numbers: 21

Python Implementation to Find the Sum of First N Natural Numbers Using Recursion

Below is the Python implementation to find the sum of the first n natural numbers using recursion:

RELATED:

Dynamic Programming: Examples, Common Problems, And Solutions

# Python implementation to find the sum of

# first n natural numbers using recursion

# Recursive function to find the sum of first n natural numbers

def findSum(n): if n<=1: return n else:

return n + findSum(n-1)

# Driver Code n1 = 5 n2 = 7 n3 = 6 print("n1: ", n1) print("n2: ", n2) print("n3: ", n3)

print("Sum of first ", n1, " natural numbers: ", findSum(n1))

print("Sum of first ", n2, " natural numbers: ", findSum(n2))

print("Sum of first ", n3, " natural numbers: ", findSum(n3))

Output: n1: 5 n2: 7 n3: 6

Sum of first 5 natural numbers: 15

Sum of first 7 natural numbers: 28

Sum of first 6 natural numbers: 21

C Implementation to Find the Sum of First N Natural Numbers Using Recursion

Below is the C implementation to find the sum of the first n natural numbers using recursion:

// C implementation to find the sum of

// first n natural numbers using recursion

#include

// Recursive function to find the sum of first n natural numbers

int findSum(int n) { if (n<=1) { return n; } else {

return n + findSum(n-1);

} } // Driver code int main() {

int n1 = 5, n2 = 7, n3 = 6;

printf("n1: %d \⁠n", n1);

printf("n2: %d \⁠n", n2);

printf("n3: %d \⁠n", n3);

printf("Sum of first %d natural numbers: %d \⁠n", n1, findSum(n1));

printf("Sum of first %d natural numbers: %d \⁠n", n2, findSum(n2));

printf("Sum of first %d natural numbers: %d \⁠n", n3, findSum(n3));

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