C# Program to Find the Sum of the Series 1 + 2 + 3 + ... + N / Sum of the First N Natural Numbers

C# programs to find the sum of the series $1 + 2 + 3 + ... + n$ i.e. the sum of the first $n$ natural numbers have been shown here. Both the iterative and recursive approaches have been shown below. The sum can also be computed using the mathematical formula $\frac{n(n+1)}{2}$.

Example:

Suppose $n = 7$

So the sum of first $7$ natural numbers = $1 + 2 + 3 + 4 + 5 + 6 + 7 = 28$

By using the mathematical formula, we obtain the sum of first $7$ natural numbers = $\frac{7 \cdot (7+1)}{2} = 28 $

The algorithm, pseudocode and time-complexity of the program have also been covered in the following sections.

Page content(s):

1. Algorithm

2. Pseudocode

3. Time Complexity

4. Program & output:

 4.1. Using formula

 4.2. Iterative approach

 4.3. Recursive approach

1. Algorithm to find sum of the series 1 + 2 + 3 + ... + n / Sum of the First N Natural Numbers

1. Take number of terms $n$ as input.

2. Set $sum = 0$.

3. Add each $i \in [1, n]$, to $sum$.

4. Display $sum$ as output.

2. Pseudocode to find sum of the series 1 + 2 + 3 + ... + n / Sum of the First N Natural Numbers

Input: Number of terms $n$

Output: Sum of $1+2+3+...+n$

1. Procedure sumSeries($n$):

2. $sum \leftarrow 0$:

3. Repeat for each $i \in [1, n]$:

4. $sum \leftarrow sum + i$

5. Return $sum$

6. End Procedure

3. Time complexity to find sum of the series 1 + 2 + 3 + ... + n / Sum of the First N Natural Numbers

Time Complexity: O(n)

Here $n$ is the number of terms.

Time Complexity (Using formula): O(1)

4. Program & output to find the sum of the series 1 + 2 + 3 + ... + n / Sum of the First N Natural Numbers

4.1. C# Program & output to find sum of the series 1 + 2 + 3 + ... + n / Sum of the First N Natural Numbers using formula

Code has been copied

/******************************************
	     alphabetacoder.com
C# Program to find sum of series 1+2+3+...
 + n using the formula n(n + 1) / 2  
*******************************************/

using System;
namespace SumofSeries {
    class Program {
        static void Main(string[] args) {
            // delclare variables
            int n, sum;

            // take input
            Console.Write("Enter no of terms: ");
            n = Convert.ToInt32(Console.ReadLine());

            // calculate the sum using formula
            sum = (n * (n + 1)) / 2;

            // display result
            Console.WriteLine("Sum: " + sum);

            // wait for user to press any key
            Console.ReadKey();
        }
    }
}

Output

Enter no of terms: 10

Sum: 55

4.2. C# Program to find sum of the series 1 + 2 + 3 + ... + n / Sum of the First N Natural Numbers using iteration

Code has been copied

/*********************************
	alphabetacoder.com
 C# Program to find sum of series
 1+2+3+...+ n using iteration 
**********************************/

using System;
namespace SumofSeries {
    class Program {
        static void Main(string[] args) {
            // delclare variables
            int n, sum = 0, i;

            // take input
            Console.Write("Enter no of terms: ");
            n = Convert.ToInt32(Console.ReadLine());

            // calculate the sum iteration
            for (i = 1; i <= n; i++)
                sum += i;

            // display result
            Console.WriteLine("Sum: " + sum);

            // wait for user to press any key
            Console.ReadKey();
        }
    }
}

Output

Enter no of terms: 150

Sum: 11325

4.3. C# Program to find sum of the series 1 + 2 + 3 + ... + n / Sum of the First N Natural Numbers using recursion

Code has been copied

/*********************************
	 alphabetacoder.com
 C# Program to find sum of series
 1+2+3+...+ n using recursion 
**********************************/

using System;
namespace SumofSeries {
    class Program {
        // recursive function to calculate sum
        // of series 1 + 2 + 3 ... + n
        int calculate_sum(int n) {
            // exit condition of recursive call
            if (n == 0)
                return 0;

            // call function
            return n + calculate_sum(n - 1);
        }

        static void Main(string[] args) {
            // delclare variables
            int n;

            // declare object
            Program obj = new Program();

            // take input
            Console.Write("Enter no of terms: ");
            n = Convert.ToInt32(Console.ReadLine());

            // display result by calling the 
            // recursive function 
            Console.WriteLine("Sum: " + obj.calculate_sum(n));

            // wait for user to press any key
            Console.ReadKey();
        }
    }
}

Output

Enter no of terms: 5

Sum = 15