number crunch!

[mr. piper]

If you needed to add all the numbers from 0 to x you can do it by pairing i.e. 1 to 100 is 100+1=101,2+99=101 3+98=101 and so forth then multiply 101 by the number of pairs - 50.so the total is 5050. you can do this with any number range including odd numbers when you have a final odd number to add to the total of pairs. Can anyone else suggest another of these short cuts concerning large numbers? (i bet no one answers this)

[Loosehead]

To add all the numbers from 1 to N:

((N+1)/2)xN)

So 1 to 10 = 5.5 x 10 = 55

I'm sure some mathmetician can make it even simpler!

[tony1941]

Can't get any simpler.  It's still burned in my brain from school: The sum of the first n natural numbers is equal to "n over 2 times n plus 1" (that, of course was in the good old days before schools had vending machines!

PS That's twice you've lost the bet!

[Peter Pedant]

gauss apparently noticed this at age 11

when his class was told to sum the numbers 1 - 100

So that's a third time you lose your bet.

[Loosehead]

There is a deafening silence from the Piper camp!