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An interesting mathematical property

  1. Aug 1, 2011 #1
    3^3 = [3^3 - 3^2] +[3^2 - 3^1] + [3^1 - 3^0] + 3^0

    Practical Demonstration:

    27 = [27-9] + [9-3] + [3-1] + 1

    27 = 18 +6+2+1

    27 = 27

    Is this property discussed in theory of games?
     
  2. jcsd
  3. Aug 1, 2011 #2
    I don't understand. What does this have to do with game theory?
     
  4. Aug 1, 2011 #3

    gb7nash

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    I'm not sure how this has anything to do with game theory, but what you just found is what's called the collapsing sum.
     
  5. Aug 1, 2011 #4
    What is that, exactly? I'm unclear on what the "interesting property" is. Obviously you can express any number as a sum of differences between a series of smaller numbers. I tried googling "collapsing sum" but found nothing helpful.
     
  6. Aug 1, 2011 #5

    micromass

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    I think he means a telescoping series: http://en.wikipedia.org/wiki/Telescoping_series of which the OP gave a (trivial) example.
     
  7. Aug 1, 2011 #6

    gb7nash

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