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Math Help - CHESSBOARD PIECE OF WORK

  1. #1
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    CHESSBOARD PIECE OF WORK

    Hi,

    I am helping my son do some maths homework. We have worked out that there are 204 squares on a chessboard, and we have worked out that this is relative to square numbers.

    How can I express a formula tidily? Is there a function that is similar to Factorial but using addition? EG: x=n+(n+1)... (n+7) simplified to a tidier function (where n = 8)?

    The formulae for a chessboard is x=1+2+3+4+5+6+7+8, so how can I use this using n? eg: something like x=(n)! but without factorial and with the appropriate function?
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  2. #2
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    I am not really sure I follow your question.
    But it is well known that \sum\limits_{k = 1}^N {k^2 } = \frac{{N\left( {N + 1} \right)\left( {2N + 1} \right)}}{6}.

    If 1 < J < N then J^2 + \left( {J + 1} \right)^2 +  \cdots + \left[ {J + (N - J)} \right]^2 = \sum\limits_{k = J}^N {k^2 } = \sum\limits_{k = 1}^N {k^2 } - \sum\limits_{k = 1}^{J - 1} {k^2 } .
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  3. #3
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    Talking

    Thanks, I'll try to re-phrase...

    x=(n)! (where n = 8)
    expands to...
    x=1*2*3*4*5*6*7*8

    Can I use any function to do similar but using addition instead of multiplication eg...
    x=1+2+3+4+5+6+7+8
    so x = 204

    Basically, a formula that works out how many squares a grid of any given size contains. EG: 8*8 grid has 204 possible squares within it (1, 2, 3, 4, 5, 6, 7, 8)

    Is this any clearer?




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  4. #4
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    Quote Originally Posted by danielmegson View Post
    x=1+2+3+4+5+6+7+8
    so x = 204

    Basically, a formula that works out how many squares a grid of any given size contains. EG: 8*8 grid has 204 possible squares within it (1, 2, 3, 4, 5, 6, 7, 8)

    Is this any clearer?
    It was clear the first time for the sum.
    It is after all a sum and not a product.
    I gave you the formula for the sum.
    This is a well known problem and you have been given the solution twice on this board.
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  5. #5
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    Thanks, sorry I'm a bit rusty at mathematics - been a long while! Thanks for your help!
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