Project Euler, Problem 6: Sum Square Difference

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

1^{2} + 2^{2} + \dots + 10^{2} = 385

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

{(1 + 2 + \dots + 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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Average: 0 Runs: 0

SD: 0 ms

Max: 0

Min: 1000

The sum of squares 1 – n is the nth pyramid number. Likewise the square of the sum of 1 – n is the square of the nth triangle number.

Triangle numbers and pyramid numbers are easy to compute so I can just take the difference once I know which triangle/pyramid number I'm dealing with.

Triangle number formula:

\frac{n (n + 1)}{2}

Pyramid number formula:

\frac{n (n+1)(2n+1)}{6}