Python Program to Find Sum of n Natural Numbers

You can find the sum of n natural numbers in Python using the formula sum = n * (n + 1) // 2 or by looping from 1 to n and adding each number.

Examples

Input5

Output15

Input10

Output55

Input1

Output1

How to Think About It

To find the sum of the first n natural numbers, think of adding all numbers from 1 up to n. You can do this by adding each number one by one or use a simple math formula that calculates the total quickly without adding each number.

Algorithm

1

Get the input number n from the user.

2

Use the formula sum = n * (n + 1) // 2 to calculate the sum.

3

Print the result.

Code

python

n = int(input("Enter a positive integer: "))
sum_natural = n * (n + 1) // 2
print("Sum of", n, "natural numbers is:", sum_natural)

Output

Enter a positive integer: 5
Sum of 5 natural numbers is: 15

Dry Run

Let's trace the example where n = 5 through the code

1

Input

User enters n = 5

2

Calculate sum

sum_natural = 5 * (5 + 1) // 2 = 5 * 6 // 2 = 30 // 2 = 15

3

Output

Print 'Sum of 5 natural numbers is: 15'

n	Calculation	sum_natural
5	5 * (5 + 1) // 2	15

Why This Works

Step 1: Input number

We get the number n from the user to know how many natural numbers to add.

Step 2: Use formula

The formula n * (n + 1) // 2 quickly calculates the sum without looping.

Step 3: Print result

We show the sum to the user with a clear message.

Alternative Approaches

Using a loop

python

n = int(input("Enter a positive integer: "))
sum_natural = 0
for i in range(1, n + 1):
    sum_natural += i
print("Sum of", n, "natural numbers is:", sum_natural)

This method is easy to understand but slower for very large n compared to the formula.

Using recursion

python

def sum_natural(n):
    if n == 1:
        return 1
    else:
        return n + sum_natural(n - 1)

n = int(input("Enter a positive integer: "))
print("Sum of", n, "natural numbers is:", sum_natural(n))

Recursion is elegant but can cause stack overflow for very large n.

Complexity: O(1) time, O(1) space

Time Complexity

Using the formula takes constant time because it does a fixed number of operations regardless of n.

Space Complexity

The formula uses only a few variables, so space is constant.

Which Approach is Fastest?

The formula method is fastest and most efficient compared to looping or recursion.

Approach	Time	Space	Best For
Formula	O(1)	O(1)	Fastest for any n
Loop	O(n)	O(1)	Easy to understand, small n
Recursion	O(n)	O(n)	Learning recursion, small n