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.

## 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)

## 4.1. 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: ");

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

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

// wait for user to press any key
}
}
}


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: ");

// 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
}
}
}


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: ");

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

// wait for user to press any key