Problem 6

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.

#!/usr/bin/ruby
number = 100
# Sum of the first n natural numbers 
# sum_n = n(n+1)/2
def sumNumbers(n)
	return (n * (n + 1) / 2)
end
# Sum of squares of the first n natural numbers 
# sum^2_n = n(n+1)(2n+1)/6
def sumSquaredNumbers(n)
	return ((n * (n + 1) * (2 * n + 1)) / 6)
end
sum = sumNumbers(number)
squared = sumSquaredNumbers(number)
puts (sum * sum - squared).to_s