Aside - a long time ago, I worked on a high school math problem which involved summing the thousand fractions 0/1, 1/2, 2/3,...upto 999/1000, so I did the obvious iteration.

(display (foldl + 0 (map (lambda (x) (/ x (+ x 1))) (range 0 1000))))

The solution matched and I was happy. Then I thought wouldn't it be neat to do this in a dozen languages and benchmark...but got nowhere with that idea. None of the languages supported fraction addition without jumping through whole bunch of hoops. I wonder if its still the same situation. If someone wants to give this a shot, the answer if you do this for the first ten is 17819/2520.

In Haskell the numerator and denominator of the Rational type are unbounded integers, so one of the (many equivalent) ways of writing it is:

    ghci> sum [i % (i+1) | i <- [0..9]]
    17819 % 2520
    ghci> 

I'll spare people the full result, but:

    ghci> sum [i % (i+1) | i <- [0..999]]
    70755...77483 % 71288...20000
    ghci>