1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Series (proof) question

  1. Feb 22, 2015 #1
    iiii(a-1)!iiiiiiiiiiiiii(a-1)!iiiiiiiiiiiii(a-1)!iiiiiiiiiiiiiiiiii(a-1)!
    ------------ii+ii------------ii+ii------------iiiiiii+ii------------ii=ii2a-1
    i(a-1)!*0!iiiiiiiiii(a-2)!*1!iiiiiiiii(a-3)!*2!iiii...iiiiiii0!*(a-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 #
    iii(x+y-2)!
    ---------------
    (x-1)!*(y-1)!
    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

    Svein

    User Avatar
    Science Advisor

    [itex] 2^{a-1}=(1 + 1)^{a-1} =1^{a-1}+\frac{a-1}{1}1^{a-2}1^{1}+...[/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Series (proof) question
  1. Series Proofs (Replies: 5)

  2. Proof of a series (Replies: 2)

  3. Divergent Series Proof (Replies: 2)

Loading...