Problem 6

Problem Statement

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

$$1^2 + 2^2 + ... + 10^2 = 385$$The square of the sum of the first ten natural numbers is,

$$(1 + 2 + ... + 10)^2 = 55^2 = 3025$$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 one hundred natural numbers and the square of the sum.

Approach

Python implementation

```
````import math`

`res = 0`

`def sum_of_squares(x):`

` res = 0`

` for i in range(1,x+1):`

` res = res + i*i`

` return res`

`def square_of_sum(x):`

` tmp = (x * (x + 1)) / 2`

` return tmp * tmp`

`res = int(square_of_sum(100) - sum_of_squares(100))`

`print("Answer is " + str(res))`

You can also download the source code for this problem here and compile it on your local machine.

Further Analysis