Gauss

The famous mathematician, Carl Friedrich Gauss. figured this out when he was a kid in school...
His teacher asked his class to add up all the numbers from 1 to 100.
Gauss figured out that the numbers on opposite ends added up to 101. (i.e. 1+100=101, 2+99=101, 3+98=101, etc...) and since this pairing would occur 50 times due to 100/2=50, the addition of all the numbers could be figured out by 50x101 = 5050. This is a faster than doing 1+2+3+4+...+100=5050.
Gauss figured this out in minutes, and impressed the shit out of everyone.

Its a good story. Gauss was sort of a dick, but he discovered some important shit.