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Homework Help: Series (proof) question

  1. Feb 22, 2015 #1

    In case you are having trouble reading that:
    [itex](a-1)!/((a-1!*0!)) + (a-1)!/((a-2)!*1!) + (a-1)!/((a-3)!*2!)... + (a-1)!/(0!*(a-1)!) = 2a-1[/itex]
    Assuming a = positive integer

    Essentially, I haven't had much experience with logs, and would be interested in a hint to making this a little more workable.

    The next part incorporates part of a logic problem. If you haven't completed (click here), don't continue
    Each term represents a number of combinations that occurs with a specific number of objects. For example, if you have 10 people and want to find out how many combinations there are of them going to a party (1,6,10), (1,3,5,9,10) etc; you can find out by finding how many different combinations of 1 person there are, how many combinations of two people, etc. Essentially, I developed a chart to represent it:
    1 1 1 1
    1 2 3 4
    1 3 6 10
    1 4 10 20

    And a formula to find any term where x=row # and y=column #
    The series above represents a sum of the diagonal of the chart. Someone else also noticed that the same problem could be solved using binary, hence the fact that they equal each other.
    I can go into more detail about how I developed this if requested
    Last edited: Feb 22, 2015
  2. jcsd
  3. Feb 22, 2015 #2


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    [itex] 2^{a-1}=(1 + 1)^{a-1} =1^{a-1}+\frac{a-1}{1}1^{a-2}1^{1}+...[/itex]
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