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