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Math Help - what is this called and what purpose does it serve?

  1. #1
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    Question 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?
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  2. #2
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    You will use that sort of thing for finding limits and for series. That's not until Precalc.
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  3. #3
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    Quote Originally Posted by Hollysti View Post
    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
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  4. #4
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    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 . = . 8 - 1
    . . . . . . .12 x 14 .= .168 .= .13 - 1

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

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