# what is this called and what purpose does it serve?

• Sep 10th 2006, 11:39 PM
Hollysti
what is this called and what purpose does it serve?
I have proven that if you have any 4 consecutive numbers (n, n+1, n+2, n+3) then (n+1)(n+2)=(n)(n+3)+2, but is this used for anything and if it is what is it called?
• Sep 11th 2006, 04:20 AM
dnlstffrd
You will use that sort of thing for finding limits and for series. That's not until Precalc.
• Sep 11th 2006, 04:28 AM
CaptainBlack
Quote:

Originally Posted by Hollysti
I have proven that if you have any 4 consecutive numbers (n, n+1, n+2, n+3) then (n+1)(n+2)=(n)(n+3)+2, but is this used for anything and if it is what is it called?

It is a special case of the formula for the sum of an arithmetic progression.

Look at Arithmetic progression - Wikipedia, the free encyclopedia

RonL
• Sep 11th 2006, 06:32 AM
Soroban
Hello, Holly!

Quote:

I have proven that if you have any 4 consecutive numbers (n, n+1, n+2, n+3)
then (n+1)(n+2) = (n)(n+3)+2, but is this used for anything
and if it is, what is it called?

With four consecutive numbers, the product of the "inner two"
. . is always 2 greater than the product of the "outer two".

As far as I know, this does not have a name nor a particular use.
. . But it is an interesting fact.

A similar phenomenon:

If two integers differ by 2, their product is one less than a perfect square.

Examples: .7 x 9 .= . 63 . = . 8² - 1
. . . . . . .12 x 14 .= .168 .= .13² - 1

This is glaringly obvious when we see: .(n - 1)(n + 1) .= .n² - 1