Python Program to calculate Sum of Series 1²+2²+3²+….+n²

Write a Python Program to calculate Sum of Series 1²+2²+3²+….+n² using For Loop and Functions with an example.

The Mathematical formula for Python Sum of series 1²+2²+3²+….+n² = ( n (n+1) (2n+1)) / 6

Python Program to calculate Sum of Series 1²+2²+3²+….+n²

This Python program asks the user to enter any positive integer. Next, the Python program finds the sum of series 1² + 2² + 3² + … + n² using the above formula.

# Python Program to calculate Sum of Series 1²+2²+3²+….+n²
 
number = int(input("Please Enter any Positive Number  : "))
total = 0

total = (number * (number + 1) * (2 * number + 1)) / 6

print("The Sum of Series upto {0}  = {1}".format(number, total))

OUTPUT

ANALYSIS

Sum = (Number * (Number + 1) * (2 * Number + 1 )) / 6
Sum = (6 * (6 + 1) * (2 * 6 +1)) / 6 => (6 * 7 * 13) / 6
and the output, Sum = 91

Python Program to calculate Sum of Series 1²+2²+3²+….+n² Example 2

If you want the Python to display the series order 1² + 2² + 3² +4² + 5^2, we have to add extra For Loop along with If Else

# Python Program to calculate Sum of Series 1²+2²+3²+….+n²
 
number = int(input("Please Enter any Positive Number  : "))
total = 0

total = (number * (number + 1) * (2 * number + 1)) / 6

for i in range(1, number + 1):
    if(i != number):
        print("%d^2 + " %i, end = ' ')
    else:
        print("{0}^2 = {1}".format(i, total))

OUTPUT

Python Program to calculate Sum of Series 1²+2²+3²+….+n² using Functions

This Python Sum of Series 1²+2²+3²+….+n² program is the same as above. But in this Python program, we are defining a Functions to place logic.

# Python Program to calculate Sum of Series 1²+2²+3²+….+n²
 
def sum_of_square_series(number):
    total = 0

    total = (number * (number + 1) * (2 * number + 1)) / 6

    for i in range(1, number + 1):
        if(i != number):
            print("%d^2 + " %i, end = ' ')
        else:
            print("{0}^2 = {1}".format(i, total))


num = int(input("Please Enter any Positive Number  : "))
sum_of_square_series(num)

OUTPUT

Python Program to calculate Sum of Series 1²+2²+3²+….+n² using Recursion

Here, we are using the Python Recursive function to find the Sum of Series 1²+2²+3²+….+n².

# Python Program to calculate Sum of Series 1²+2²+3²+….+n²
 
def sum_of_square_series(number):
    if(number == 0):
        return 0
    else:
        return (number * number) + sum_of_square_series(number - 1)


num = int(input("Please Enter any Positive Number  : "))
total = sum_of_square_series(num)

print("The Sum of Series upto {0}  = {1}".format(num, total))

OUTPUT