# C++ Program to Find the Sum of First N Natural Numbers # Program to find sum of first  N natural numbers

We know that Natural number is integer number which start from 1,2,3,4…… and so on.

So we will calculate the First N natural number

In the sum of first N natural number user gave the value of N. If the value is 6 then process is following

1+2+3+4+5+6 = 21

Here we will see two different methods to do find sum of first n natural numbers. One is by using formula whose time complexity is O(1) and other is by using for loop whose time complexity is O(n).

## Algorithm

• Step 1. Start
• Step 2. Enter a number (N).
• Step 3. Use formula to calculate the sum of N natural number || Sum=(n*(n+1))/2.
• Step 4. Print sum of N Natural Number.
• Step 5. Stop

## C++ Code

```#include
using namespace std;
int main()
{
//Declare variable sum and n
int sum = 0, n;

//Take input from user
cout<<"Enter the first N Natural Number\n"; cin>>n;

sum=(n*(n+1))/2;

cout<<"Sum is "<<sum;

//End of program
return 0;

}
```

### Output

```Enter the first N Natural Number
3
Sum is 6
```

## Time complexity

The time complexity of this program is O(1).

## Auxiliary Space

The auxiliary space of this program is O(1)

## Formula used

We have used formula (n*(n+1))/2 to find answer in O(1).

Let n=3

sum=1+2+3=6

Using formula : (3*4)/2=12/2=6

Hence we are getting same answer using formula as well.

## Algorithm:-

Step 1 : Ask the user to enter a  number which will denote the limit.

Step 2 : Declare a variable to store the addition and initialize it with 0.

Step 3 : Use a loop to perform iterations for adding natural numbers from 1 till the limit entered by the user.

Step 4 : Use a statement for addition purpose.

Step 5 : Print the result.

### C++ Code:-

```#include
using namespace std;
int main()
{
//for initialize variable
int Number, i, Sum = 0;
//to take user input
cout<<"\n Kindly Insert an Integer Variable\n"; cin>>Number;

//use for loop for these condition
for(i = 1; i <= Number; i++)
{
Sum = Sum + i;
}

//display
cout<<"Sum of Natural Numbers: "<< Sum;

return 0;
}
```

### Output

```Kindly Insert an Integer Variable
4
Sum of Natural Numbers: 10```

## Time complexity

The time complexity of this program is O(n).

## Auxiliary Space

The auxiliary space of this program is O(1)