http://projecteuler.net/index.php?section=problems&id=6

euler-006

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.

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sum of squares:

$ perl -e '$a = 0; foreach $i (1..100) { $a += $i * $i } print "$a\n"'
338350

square of sum:

SUM(1...n) = n(n + 1) / 2
SUM(1...100) = 100 * 101 / 2 = 10100 / 2 = 5050
squaring that: = 5050 * 5050 = 25502500

difference = 25502500 - 338350 = 25164150