In this article, we will learn about python program to find sum of N Natural Numbers.

Getting Started

The task is to find the sum of N natural numbers using python program. For example,

If N = 10, then output should be 55 because sum of first N natural numbers in 55 i.e. 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55.

If N = 5, then output should be 15 because 1 + 2 + 3 + 4 + 5 = 15.

We can do it in below ways –

1. Using for loop
2. Using Arithmetic Formula
3. Using Recursion
4. Using sum() and list Comprehension
5. Using While Loop
6. Using math.comb() Function

Using for loop

We can simply run a python for loop to find sum of N natural numbers as shown below –

def sum_of_n_numbers(n):
    sum = 0
    for i in range(1, n + 1):
        sum += i
    return sum


# Get user input for N

n = int(input("Enter a positive integer N: "))
result = sum_of_n_numbers(n)
print(f"The sum of the first {n} natural numbers is: {result}")

Here,

• Initialise a variable – sum by 0.
• Run a for loop from 1 to n.
• In each iteration, add iteration value in sum. For example, in ith iteration, add i in sum.
• Using this way, we will finally get sum of all values from 0 to n.
• Finally, result is printed using print() function.

Output:

Enter a positive integer N: 
12
The sum of the first 12 natural numbers is: 78

Using Arithmetic Formula

There is an arithmetic formula

Sum of N Natural numbers = n * (n + 1) / 2

We can use this arithmetic formula to write python program to find sum of n natural numbers. This best way to find sum of n natural numbers in python program.

def sum_of_n_numbers(n):
    return int(n * (n + 1) / 2)

# Get user input for N
n = int(input("Enter a positive integer N: "))
result = sum_of_n_numbers(n)
print(f"The sum of the first {n} natural numbers is: {result}")

Here,

• sum_of_n_numbers method returns sum of N natural numbers.
• Finally, we print the result using print() function.

Output:

Enter a positive integer N: 
5
The sum of the first 5 natural numbers is: 15

Using Recursion

We can write program to find sum of N natural numbers recursively too. It’s just a recursive approach of for loop program.

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

# Get user input for N
n = int(input("Enter a positive integer N: "))
result = sum_of_n_numbers(n)
print(f"The sum of the first {n} natural numbers is: {result}")

Here,

• sum_of_n_numbers method is getting called recursively until the last value 1.
• In the last call, this method will return 1.
• After that, second last call will be executed. In this call, 1 + 2 will be returned.
• Subsequently, all method calls will be executed and we will get sum of n numbers.

Output:

Enter a positive integer N: 
4
The sum of the first 4 natural numbers is: 10

Using sum() and list Comprehension

Built-in method sum() returns sum of numbers provided as arguments. We can use sum() method too to write python program to find sum of N natural numbers.

def sum_of_n_numbers(n):
    return sum([i for i in range(1, n + 1)])

# Get user input for N
n = int(input("Enter a positive integer N: "))
result = sum_of_n_numbers(n)
print(f"The sum of the first {n} natural numbers is: {result}")

Here,

• sum() method takes list of values as arguments.
• range() method returns immutable sequence numbers between specified start and stop value. Here, it’s between 1 and (n + 1)

Output:

Enter a positive integer N: 
10
The sum of the first 10 natural numbers is: 55

Using while Loop

Instead of python for loop, we can also use python while loop to find sum of N natural numbers as shown below –

def sum_of_n_numbers(n):
    sum = 0
    i = 1
    while i <= n:
        sum += i
        i += 1
    return sum

# Get user input for N
n = int(input("Enter a positive integer N: "))
result = sum_of_n_numbers(n)
print(f"The sum of the first {n} natural numbers is: {result}")

Here,

• sum_of_n_numbers method returns sum of N natural numbers using while loop.
• At first, initialise sum = 0, i = 1.
• Now, run a while loop from i = 1 to i = n.
• In each iteration, add value of i to sum. Then, increment the value i by 1.
• Finally, we get value of variable sum as sum of N natural numbers.
• Returned value is then printed using print() method.

Output:

Enter a positive integer N: 
10
The sum of the first 10 natural numbers is: 55

Using reduce() Function

reduce() function applies a function to the elements of iterable. We can use this trick to write python program to find sum of N natural numbers as shown below –

from functools import reduce

def sum_of_n_numbers(n):
    return reduce(lambda x, y: x + y, range(1, n + 1))

# Get user input for N
n = int(input("Enter a positive integer N: "))
result = sum_of_n_numbers(n)
print(f"The sum of the first {n} natural numbers is: {result}")

Output:

Enter a positive integer N: 
12
The sum of the first 12 natural numbers is: 78

Using math.comb() Function

math.comb() is basically a built-in method in math module in python. math.comb(n, k) returns number of ways to choose k items from n without repetition and without order.

Mathematically, math.comb(n, k) is equivalent to n! / (k! * (n – k)!).

So, math.comb(n + 1, 2) is equivalent to

=> (n + 1)! / (2! * ((n + 1) – 2)!)
=> (n + 1)! / (2! * ((n – 1)!)
=> (n + 1) * n * (n – 1)! / (2 * 1 * (n – 1)!)
=> (n + 1) * n * (n – 1)! / (2 * (n – 1)!)
=> (n + 1) * n / 2

Notice that it’s same formula which we have used earlier in this article.

import math

def sum_of_n_numbers(n):
    return math.comb(n + 1, 2)

# Get user input for N
n = int(input("Enter a positive integer N: "))
result = sum_of_n_numbers(n)
print(f"The sum of the first {n} natural numbers is: {result}")

Output:

Enter a positive integer N: 
10
The sum of the first 10 natural numbers is: 55

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