[Luzion]

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...