[Luzion]

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Heres an easy way to add up a sequence of numbers. For example, lets say from 1 to 100.
1 + 2 + 3 + 4 + 5 + 6 ..... + 100 = ?

The sum of the first and last number, which is 1 + 100 = 101.
The sum of the second and second to last number, which is 2 + 99 = 101.
The sum of the third and third to last number, which is 3 + 98 = 101.

Get the pattern? Summation of two numbers that equal 101 occurs 50x in this sequence. 1+100, or 2+99, or 3+98, or 4+97, or 5+96...

1 + 2 + 3 + 4 + 5 + 6 + 7 .... + 100 = 101 x 50 = 5050

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 11 x 5 = 55

Summation of

1 to 1000 = 1001 x 500 = 50050
17 to 9862 = 9879 x 4923 = 48,634,317

Its a neat idea, and could be fairly useful...

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Good job Gauss.

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well hey, no one ever said it was an original shortcut... [img]/images/graemlins/grin.gif[/img]

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Gauss came up with it when he was five.

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I guess you are familar with the story of how one of his teachers gave the same problem to his class to occupy them for awhile, and he solved it right away using the method I just explained. Blah... [img]/images/graemlins/tongue.gif[/img]