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Math Help - Sequence of numbers

  1. #1
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    Unhappy Sequence of numbers

    I have a number theory problem with solution but i dont understand why one can write this equallity (green question mark). Because 1122 is not 11*22 or 111222 is not 111*222.
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Sequence of numbers

    The attachment has a typo. It should be:

     11..122...2 = \frac 1 9 (10^{2n} - 10^n) + \frac 2 9 (10^n - 1)

    The rest is correct. For example, starting with 1122 (n=2) you have:

     1122 = 1100 + 22 = \frac 1 9 9900 + \frac 2 9 99 = \frac 1 9 (10^4 - 10^2) + \frac 2 9 (10^2 -1)
     = \frac 1 9 (10^4 +10^2 - 2) = \frac 1 9 (10^2-1)(10^2+2) = \frac 1 9 99 \cdot 102 = 33 \cdot 34
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  3. #3
    Member agentmulder's Avatar
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    Re: Sequence of numbers

    To me it looks like the expression immediately after the green question mark and before the next equal sign...

    1/9(10^n -1).2/9(10^n -1)

    i think that dot separates 1's and 2's

    Examples: n = 1

    1/9(9).2/9(9) = 1.2, '1 dot 2' or twelve

    n = 2

    1/9(99).2/9(99) = 11.22, '11 dot 22' or 1122

    n = 3

    1/9(999).2/9(999) = 111.222, '111 dot 222' or 111222

    Am I stretching it too much?



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  4. #4
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    Re: Sequence of numbers

    Thank you very much. You have nice brains.
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  5. #5
    MHF Contributor ebaines's Avatar
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    Re: Sequence of numbers

    Quote Originally Posted by agentmulder View Post
    i think that dot separates 1's and 2's
    ...
    1/9(999).2/9(999) = 111.222, '111 dot 222' or 111222

    Am I stretching it too much?
    Nice idea - but yes, you are stretching it too much! By convention the "dot" symbol means multiplication. Thus:

    11 \cdot 22 = 11 \times 22 = 242
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