# Project Euler

## Sum square difference

### Problem 6

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

1

^{2}+ 2^{2}+ … + 10^{2}= 385The square of the sum of the first ten natural numbers is,

(1 + 2 + … + 10)

^{2}= 55^{2}= 3025Hence 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.

Finally, something looks familiar. Remember Problem 1 and the summation formula. Instead of O(n) complexity, simply apply the summation formula to get O(1) complexity for this problem as follow:

The summation of was discussed previously in Problem 1 as:

The summation of is: