Project Euler #6 in Ruby

Question

Question:

Difference between the Sum of squares from 1 to 100 and the square of sums of 1 to 100.

Answer in Ruby:

range.inject(:+) ** 2 - range.map{|x| x ** 2}.inject(:+)

This one seems pretty straightforward but welcome any improvements to make it more elegant!

Answer 1

The elegance of Mathematics:

def sum_below(n)
 n * (n + 1) / 2
end
def sum_squares_below(n)
 n * (n + 1) * (2*n + 1) / 2
end
limit = 1000
puts sum_below(limit) ** 2 - sum_squares_below(limit)

The Math under n * (n + 1) / 2

We have some natural numbers and we want to find their sum, the list is:

1, 2, 3, 4 ... n

Now we can note that the sum of n + 1 is equal to the sum (n - 1) + (1 + 1) and is in turn equal to (n - 1 - 1) + (1 + 1 + 1). In practice in the following

1, 2, 3, 4, 5, 6

We can see that 1 +たす 6 =わ=わ 2 +たす 5 =わ=わ 3 +たす 4 =わ=わ 7.

We must repeat this (sum that equals n + 1) (n / 2) times so we arrive to the final formula:

sum_below(n) = (n + 1) * n / 2

• Sakamoto Kazuma: Shouldn't the sum_squares_below actually be n * (n + 1) * (2*n + 1) / 6 ?