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

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In this article, we will show you, How to write a Python Program to calculate Sum of Series 1²+2²+3²+….+n² using For Loop and Functions with example.

The Mathematical formula for 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 allows user is asked to enter any positive integer. Next, this program will find 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

Python Program to calculate Sum of Series 1²+2²+3²+….+n² 1

ANALYSIS

Sum = (Number * (Number + 1) * (2 * Number + 1 )) / 6
Sum = (6 * (6 + 1) * (2 * 6 +1)) / 6 => (6 * 7 * 13) / 6
Sum = 91

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

If you want to display the series order 12 + 22 + 32 +42 + 52 , 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 2

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

This program is same as above but this time we are defining function 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 3

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

Here, we are using Recursive function concept

# 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

Python Program to calculate Sum of Series 1²+2²+3²+….+n² 4