Thread: 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?

You will use that sort of thing for finding limits and for series. That's not until Precalc.

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

Hello, Holly!

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