In this post, We will see how to write a python program for finding Sum of squares of first n natural numbers in different ways.

Example:

Input: N = 2
Output: 1 * 1 + 2 * 2 => 5 OR 
12 + 2 2 => 5

Input: N = 3
Output: 1 * 1 + 2 * 2 + 3 * 3 => 14 OR
12 + 2 2 + 3 2 => 14

Now, Let’s see the codes:

Code 1: Run a loop from 2 to N and for each i, find i ² and adding to the sum.

# first 5 natural numbers
N = 5

# initialize variable with 1
sumSquare = 1

# loop from 2 to N
for i in range(2, N + 1) :
    
    # square summation
    sumSquare += i ** 2
    
# print the result
print("Sum of the Squares of 1st", N ,
      "Natural Numbers is:",sumSquare)

Output:

Sum of the Squares of 1st 5 Natural Numbers is: 55

Code 2: Create user defined function, main and then apply the previous code logic.

# Define a user defined 
# function for finding
# sum of squares of 1st
# N natural Numbers
def sumOfSquares(Num) :

    # initialize variable with 1
    sumSquare = 1

    # loop from 2 to N
    for i in range(2, Num + 1) :

        # square summation
        sumSquare += i ** 2
        
    # return result
    return sumSquare

# main code
if __name__ == "__main__" :

    # first 5 natural numbers
    Num = 5
    
    # function calling and
    # printing the result
    print("Sum of the Squares of first", Num ,
          "Natural Numbers is:",
          sumOfSquares(Num))

Output:

Sum of the Squares of first 5 Natural Numbers is: 55

Code 3: Run a loop from 2 to N and for each i, find i * i and adding to the sum.

# Define a user defined 
# function for finding
# sum of squares of 1st
# N natural Numbers
def sumOfSquares(Num) :

    # initialize variable with 1
    sumSquare = 1

    # loop from 2 to N
    for i in range(2, Num + 1) :

        # square summation
        sumSquare += i * i
        
    # return result
    return sumSquare

# main code
if __name__ == "__main__" :

    # first 5 natural numbers
    Num = 5
    
    # function calling and
    # printing the result
    print("Sum of the Squares of 1st", Num ,
          "Natural Numbers is:",
          sumOfSquares(Num))

Output:

Sum of the Squares of 1st 5 Natural Numbers is: 55

Code 4: By Using given formula :

sum of the squares of 1st N Natural numbers:
 ((N) * (N + 1) * (2 * N + 1)) / 6

# Define a user defined 
# function for finding
# sum of squares of 1st
# N natural Numbers
def sumOfSquares(Num) :
    
    # return result
    return ((Num) * (Num + 1) * (2 * Num + 1)) / 6
    
# main code
if __name__ == "__main__" :

    # first 5 natural numbers
    Num = 5
    
    # function calling and
    # printing the result
    print("Sum of the Squares of 1st", Num ,
          "Natural Numbers is:",
          sumOfSquares(Num))

Output:

Sum of Squares of first 5 Natural Numbers is: 55

Code 5: By making a anonymous function.

# create a annonymous
# function for returning
# sum of squares of 1st
# N natural Numbers
sumOfSquares = lambda Num : ((Num) * (Num + 1) * (2 * Num + 1)) / 6
    
# main code
if __name__ == "__main__" :

    # first 5 natural numbers
    Num = 5
    
    # function calling and
    # printing the result
    print("Sum of the Squares of 1st", Num ,
          "Natural Numbers is:",
          sumOfSquares(Num))

Output:

Sum of the Squares of 1st 5 Natural Numbers is: 55