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Code Mathematics

Sum of n natural numbers

The concept of summing natural numbers is fundamental in mathematics. A natural number is any positive integer starting from 1. The sum of the first n natural numbers is a well-known formula and plays a vital role in various mathematical and computational applications. This article aims to explain how to calculate the sum of the first n natural numbers using C programming.

Problem Statement

Given a positive integer n, the task is to calculate the sum of the first n natural numbers. The formula for calculating this sum is: sum = 1 + 2 + 3 + ... + n.

Example

For instance, if n is 4, then the sum of the first 4 natural numbers would be 1 + 2 + 3 + 4 = 10. If n is 10, the sum would be 1 + 2 + 3 + ... + 10 = 55.

Idea to Solve

The solution involves utilizing the formula for the sum of the first n natural numbers. The formula sum = n * (n + 1) / 2 efficiently computes this sum. This formula is based on the arithmetic progression of natural numbers.

Pseudocode

function sum_natural_no(n):
    if n <= 0:
        return
    sum = n * (n + 1) / 2
    Print "Sum of", n, "natural numbers is", sum

function main():
    sum_natural_no(4)
    sum_natural_no(10)

Algorithm Explanation

  1. The sum_natural_no function takes a single parameter n.
  2. It first checks if n is less than or equal to 0. If it is, the function returns without performing any calculations.
  3. Using the formula sum = n * (n + 1) / 2, it calculates the sum of the first n natural numbers.
  4. The function then prints the calculated sum along with the provided value of n.
  5. The main function tests the sum_natural_no function with different values of n.

Code Solution

// C Program
// Sum of n natural numbers
#include <stdio.h>

//Calculate the sum of n natural numbers
void sum_natural_no(int n)
{
	if (n <= 0)
	{
		return;
	}
	// Formula 
	// n*(n+1) / 2
	long long int sum = n *(n + 1) / 2;
	//Display calculated result
	printf(" Sum of %d natural numbers is %lld\n", n, sum);
}
int main()
{
	//Test case
	sum_natural_no(4);
	sum_natural_no(10);
	return 0;
}

Output

 Sum of 4 natural numbers is 10
 Sum of 10 natural numbers is 55
// Java Program 
// Sum of n natural numbers
class MyMaths
{
	//Calculate the sum of n natural numbers
	public void sum_natural_no(int n)
	{
		if (n <= 0)
		{
			return;
		}
		// Formula 
		// n*(n+1) / 2
		long sum = n * (n + 1) / 2;
		//Display calculated result
		System.out.print(" Sum of " + n + " natural numbers is " + sum + "\n");
	}
	public static void main(String[] args)
	{
		MyMaths obj = new MyMaths();
		//Test case
		obj.sum_natural_no(4);
		obj.sum_natural_no(10);
	}
}

Output

 Sum of 4 natural numbers is 10
 Sum of 10 natural numbers is 55
//Include header file
#include <iostream>

using namespace std;
// C++ Program 
// Sum of n natural numbers
class MyMaths
{
	public:
		//Calculate the sum of n natural numbers
		void sum_natural_no(int n)
		{
			if (n <= 0)
			{
				return;
			}
			// Formula 
			// n*(n+1) / 2
			long sum = n * (n + 1) / 2;
			//Display calculated result
			cout << " Sum of " << n << " natural numbers is " << sum << "\n";
		}
};
int main()
{
	MyMaths obj = MyMaths();
	//Test case
	obj.sum_natural_no(4);
	obj.sum_natural_no(10);
	return 0;
}

Output

 Sum of 4 natural numbers is 10
 Sum of 10 natural numbers is 55
//Include namespace system
using System;
// C# Program 
// Sum of n natural numbers
class MyMaths
{
	//Calculate the sum of n natural numbers
	public void sum_natural_no(int n)
	{
		if (n <= 0)
		{
			return;
		}
		// Formula 
		// n*(n+1) / 2
		long sum = n * (n + 1) / 2;
		//Display calculated result
		Console.Write(" Sum of " + n + " natural numbers is " + sum + "\n");
	}
	public static void Main(String[] args)
	{
		MyMaths obj = new MyMaths();
		//Test case
		obj.sum_natural_no(4);
		obj.sum_natural_no(10);
	}
}

Output

 Sum of 4 natural numbers is 10
 Sum of 10 natural numbers is 55
<?php
// Php Program 
// Sum of n natural numbers
class MyMaths
{
	//Calculate the sum of n natural numbers
	public	function sum_natural_no($n)
	{
		if ($n <= 0)
		{
			return;
		}
		// Formula 
		// n*(n+1) / 2
		$sum = intval($n * ($n + 1) / 2);
		//Display calculated result
		echo " Sum of ". $n ." natural numbers is ". $sum ."\n";
	}
}

function main()
{
	$obj = new MyMaths();
	//Test case
	$obj->sum_natural_no(4);
	$obj->sum_natural_no(10);
}
main();

Output

 Sum of 4 natural numbers is 10
 Sum of 10 natural numbers is 55
// Node Js Program 
// Sum of n natural numbers
class MyMaths
{
	//Calculate the sum of n natural numbers
	sum_natural_no(n)
	{
		if (n <= 0)
		{
			return;
		}
		// Formula 
		// n*(n+1) / 2
		var sum = parseInt(n * (n + 1) / 2);
		//Display calculated result
		process.stdout.write(" Sum of " + n + " natural numbers is " + sum + "\n");
	}
}

function main()
{
	var obj = new MyMaths();
	//Test case
	obj.sum_natural_no(4);
	obj.sum_natural_no(10);
}
main();

Output

 Sum of 4 natural numbers is 10
 Sum of 10 natural numbers is 55
#  Python 3 Program 
#  Sum of n natural numbers
class MyMaths :
	# Calculate the sum of n natural numbers
	def sum_natural_no(self, n) :
		if (n <= 0) :
			return
		
		#  Formula 
		#  n*(n+1) / 2
		sum = int(n * (n + 1) / 2)
		# Display calculated result
		print(" Sum of ", n ," natural numbers is ", sum )
	

def main() :
	obj = MyMaths()
	# Test case
	obj.sum_natural_no(4)
	obj.sum_natural_no(10)

if __name__ == "__main__": main()

Output

 Sum of  4  natural numbers is  10
 Sum of  10  natural numbers is  55
#  Ruby Program 
#  Sum of n natural numbers
class MyMaths

	# Calculate the sum of n natural numbers
	def sum_natural_no(n)
	
		if (n <= 0)
		
			return
		end
		#  Formula 
		#  n*(n+1) / 2
		sum = n * (n + 1) / 2
		# Display calculated result
		print(" Sum of ", n ," natural numbers is ", sum ,"\n")
	end
end
def main()

	obj = MyMaths.new()
	# Test case
	obj.sum_natural_no(4)
	obj.sum_natural_no(10)
end
main()

Output

 Sum of 4 natural numbers is 10
 Sum of 10 natural numbers is 55
// Scala Program 
// Sum of n natural numbers
class MyMaths
{
	//Calculate the sum of n natural numbers
	def sum_natural_no(n: Int): Unit = {
		if (n <= 0)
		{
			return;
		}
		// Formula 
		// n*(n+1) / 2
		var sum: Long = (n * (n + 1) / 2).toInt;
		//Display calculated result
		print(" Sum of " + n + " natural numbers is " + sum + "\n");
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var obj: MyMaths = new MyMaths();
		//Test case
		obj.sum_natural_no(4);
		obj.sum_natural_no(10);
	}
}

Output

 Sum of 4 natural numbers is 10
 Sum of 10 natural numbers is 55
// Swift Program 
// Sum of n natural numbers
class MyMaths
{
	//Calculate the sum of n natural numbers
	func sum_natural_no(_ n: Int)
	{
		if (n <= 0)
		{
			return;
		}
		// Formula 
		// n*(n+1) / 2
		let sum: Int = n * (n + 1) / 2;
		//Display calculated result
		print(" Sum of ", n ," natural numbers is ", sum );
	}
}
func main()
{
	let obj: MyMaths = MyMaths();
	//Test case
	obj.sum_natural_no(4);
	obj.sum_natural_no(10);
}
main();

Output

 Sum of  4  natural numbers is  10
 Sum of  10  natural numbers is  55

Time Complexity

The time complexity of this code is constant, O(1), since the calculations performed inside the sum_natural_no function involve only basic arithmetic operations. The execution time remains constant regardless of the input value of n.

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