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?

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- Sep 10th 2006, 11:39 PMHollystiwhat 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 AMdnlstffrd
You will use that sort of thing for finding limits and for series. That's not until Precalc.

- Sep 11th 2006, 04:28 AMCaptainBlack
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 AMSoroban
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