# Difference Of Squares

Find the difference between the square of the sum and the sum of the squares of the first N natural numbers.

The square of the sum of the first ten natural numbers is
(1 + 2 + ... + 10)² = 55² = 3025.

The sum of the squares of the first ten natural numbers is
1² + 2² + ... + 10² = 385.

Hence the difference between the square of the sum of the first
ten natural numbers and the sum of the squares of the first ten
natural numbers is 3025 - 385 = 2640.

You are not expected to discover an efficient solution to this yourself from
first principles; research is allowed, indeed, encouraged. Finding the best
algorithm for the problem is a key skill in software engineering.

## Hints
For this exercise the following F# features come in handy:
- The [range operator](https://msdn.microsoft.com/en-us/visualfsharpdocs/conceptual/operators.%5B-..-%5D%5B%5Et%5D-function-%5Bfsharp%5D) allows you to succinctly create a range of values.
- [List.sumBy](https://msdn.microsoft.com/en-us/visualfsharpdocs/conceptual/list.sumby%5B't,%5Eu%5D-function-%5Bfsharp%5D) is a condensed format to apply a function to a list and then sum the results.


## Running the tests

To run the tests, run the command `dotnet test` from within the exercise directory.

## Autoformatting the code

F# source code can be formatted with the [Fantomas](https://github.com/fsprojects/fantomas) tool.

After installing it with `dotnet tool restore`, run `dotnet fantomas .` to format code within the current directory.

## Further information

For more detailed information about the F# track, including how to get help if
you're having trouble, please visit the exercism.io [F# language page](http://exercism.io/languages/fsharp/resources).

## Source

Problem 6 at Project Euler [http://projecteuler.net/problem=6](http://projecteuler.net/problem=6)