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Nice. How did I get the result in the first place?

I know that this sum can be expressed as a cubic polynomial. So I just evaluated the sum at four data-points (n=0,1,2,3) and used those to determine the four coefficents by solving a linear equation system.




Turns out that drawing a picture really helps: http://news.ycombinator.com/item?id=101532


You can usually come up with a clever picture only after you understood the problem - not before.




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