Sum square difference

Coding Challenge Level: Beginner

Today's challenge requires you to write code to find the sum of the squares of the first ten natural numbers is,

12?+ 22?+ ... + 102?= 385

The square of the sum of the first ten natural numbers is,

(1 + 2 + ... + 10)2?= 552?= 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 ? 385 = 2640.

Find the difference between the sum of the squares of the first?n?natural numbers and the square of the sum.

Solution:

The formula to find the difference between the sum of squares and the square of the sum of the first n natural numbers is:

(square of the sum) - (sum of the squares)

To calculate this difference, we first need to calculate the sum of the first n natural numbers and the sum of the squares of the first n natural numbers. We can use loops and mathematical formulas to do this.

Here's the Python code:

def sum_square_difference(n):
? ? sum_of_n = (n * (n+1)) // 2? # formula for the sum of first n natural numbers
? ? sum_of_squares = (n * (n+1) * (2*n+1)) // 6? # formula for the sum of squares of first n natural numbers
? ? square_of_sum = sum_of_n ** 2
? ? return square_of_sum - sum_of_squares        

The sum_square_difference function takes in a value of n and calculates the sum of the first n natural numbers and the sum of the squares of the first n natural numbers using the formulas above. Then it calculates the square of the sum of the first n natural numbers by squaring the sum of n. Finally, it returns the difference between the square of the sum and the sum of squares.

To use this function, simply call sum_square_difference and pass in the value of n as the argument. For example, to find the difference between the sum of the squares and the square of the sum of the first 10 natural numbers, you would call the function like this:

print(sum_square_difference(10))        

This would output:

2640        

So the difference between the sum of squares and the square of the sum of the first 10 natural numbers is 2640.

Similarly, to find the difference between the sum of squares and the square of the sum of the first 15 natural numbers, you would call the function like this:

print(sum_square_difference(15))        

This would output:

13160        

So the difference between the sum of squares and the square of the sum of the first 15 natural numbers is 13160.

In conclusion, if you ever need to find the difference between the sum of squares and the square of the sum of the first n natural numbers, the Python code above provides a simple and efficient solution using mathematical formulas.

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