Formula help PLEASE

C

cole92

Junior Member
Joined
Mar 30, 2006
Messages
65
Can someone help me write a formula? The question is, "Imagine a pyramid of tennis balls piled so that each layer is a square, beginning with one ball at the top and four at the next layer, nine, etc. The numbers that result when you add the number of successive layers are pyramidal numbers. The first is 1. Next layer is 4 (plus the one) =5 for the next layer, etc. How can I write a formula to find the various level numbers. (e.g) 40th layer?

Thanks in advance for your help!!
 
Each successive layer is a perfect number. Right?.

So you're adding up the perfect squares from 1 to n.


\(\displaystyle \L\\\sum_{1}^{n}k^{2}=\frac{n(n+1)(2n+1)}{6}\)


n=40 is 22140 tennis balls
 
hey, great thanks. i understand it and everything, but why do you divide by 6? i see that the equationg definitely works, but why divide by 6? thanks again
 
does anybody know why you divide this formula by 6? i dont exactly get where it comes from
 
You must log in or register to reply here.
Top