Math question

[Aaron Coffee]

At work I stack parts cut out of tubing in a pyramid, with each level having one less part than the previous level. Can someone tell me how to calculate how many parts are in a pile without adding each level (25+24+23+22+21....)? I probably had this in finite math in college, but don't remember it.
Thanks
Aaron

[Tom Kurth]

I don't know how a mathematician would do it but I would add the number in the top layer (always 1) and the number in the bottom layer (in this case 25) making 26. Multiply that by .5 less than half the number of layers (25x.5=12.5,12.5-.5=12, 12x26=312). Then add 13 for the middle layer making 325. Now, somebody else count them to see if I'm right.

Best,
Tom

[pohukai]

this sounds like a divergent series

total = (biggest row * (biggestrow+1) ) / 2

So a biggest row of 25 would be (25 * 26)/2 = 325

check this out...http://en.wikipedia.org/wiki/1_%2B_2_%2 ... _%E2%80%A6

[bikeopelli]

n(n+1)/2 where n is the largest number

[pete42]

nice answers but one I couldn't do in my head
but then Aaron didn't say he didn't have pencil and paper did he?
so nice answers

pete

[Aaron Coffee]

Do have a calculator, that equation still lot easier than adding each row. Probably could just take the computers word for how many parts it cut, but I like to work my mind and like to be thorough and double check my work.
Thanks
Aaron