Python Program for Calculating the Sum of Squares of First n Natural Numbers

In this tutorial, we will learn how to calculate the sum of squares of first n natural numbers using Python.

We have a positive integer "N", and our task is to calculate (1²+ 2² + 3² + 4² + 5² +… + N²)

Example:

Input: N = 6
Output: 91 
12 + 22 + 32 + 42 + 52 + 62 
= 1 + 4 + 9 + 16 + 25 +36
= 91

Input:  N = 2
Output: 5
12 + 22
= 1 + 4
= 5

Method 1: O(N)

In this method, a user has to run the loop from 1 to "N" natural number, and for each K, 1 <= K <= N. The user has to find the K2 to calculate the sum.

Example:

# First, we will create a function 
# which will return the sum of
# squares of first "NN"
# natural numbers
def square_sum(NN) :
  
    # here, we will iterate K from 1 
    # and NN for finding 
    # the square numbers from K to NN and
    # then add to sum.
    sum_1 = 0
    for K in range(1, NN + 1) :
        sum_1 = sum_1 + (K * K)
      
    return sum_1
  
# Driven Program
NN = int (input ("Please enter the 'N' natural number: "))
print (square_sum(NN)

Output:

Please enter the 'N' natural number:  56
60116

Method 2: O(1)

In this method, the user can calculate the sum of the square of the first "N" natural numbers by using the following formula:

For Example:

For NN = 6, sum_1 = (6 * (6 + 1) * (2 * 6 + 1)) / 6
			= (6 * (7) * (13)) / 6
			= (546) / 6
			= 91
For NN = 56, sum_1 = (56 * (56 + 1) * (2 * 56 + 1)) / 6
			  = (56 * (57) * (113)) / 6
			  = (3,60,696) / 6
			  = 60116

Code:

# First, we will create a function 
# which will return the sum of
# squares of first "NN"
# natural numbers
def square_sum(NN) :
    return (NN * (NN + 1) * (2 * NN + 1)) // 6
  
# Driven Program
NN = int( input("Please enter the 'N' natural number: "))
print (square_sum(NN))

Output:

Please enter the 'N' natural number:  87
223300

How to Avoid Early Overflow:

For the large "NN" natural number, the value of [(NN * (NN + 1) * (2 * NN + 1)) / 6] would probably overflow. The users can avoid this situation by using the fact that (NN * (NN + 1)) must be divisible by 2.

Example:

# First, we will create a function 
# which will return the sum of
# squares of first "NN"
# natural numbers
  
def square_sum(NN):
    return (NN * (NN + 1) * (2 * NN + 1)) // 3
  
# Driven Program
NN = int( input("Please enter the 'N' natural number: "))
print (square_sum(NN))

Output:

Please enter the 'N' natural number:  567
121844520

Conclusion

In this tutorial, we have explained two methods for calculating the sum of squares of "N" natural numbers using python and avoiding the code's overflow.

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