Results 1 to 4 of 4

Math Help - Binomial Theorem - Prove that result is valid only for...?

  1. #1
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
    Posts
    539

    Binomial Theorem - Prove that result is valid only for...?

    Prove that \left({m\choose 0} + {m\choose 1} - {m\choose 2} - {m\choose 3}\right) + \left({m\choose 4} + {m\choose 5} - {m\choose 6} - {m\choose 7}\right) + \mbox{...} = 0 if and only if for some positive integer k,\ m = 4k - 1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    May 2009
    From
    Tokyo, Japan
    Posts
    46
    try it for small m, and use that (m n) = (m m-n) should be pretty obvious that if the condition doesn't hold the series doesn't 'telescope' into itself and leaves a remainder.
    try the telescoping for small m if u want to see what's happening.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member pankaj's Avatar
    Joined
    Jul 2008
    From
    New Delhi(India)
    Posts
    318
    \binom{n-1}{r-1}+\binom{n-1}{r}=\binom{n}{r}<br />
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    May 2009
    From
    Tokyo, Japan
    Posts
    46
    no real need for that, just need that (7 0) = (7 7), (7 1) = (7 6) etc.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove by using Binomial Theorem
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: September 20th 2010, 03:33 AM
  2. Prove result for binomial coefficients?
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: June 10th 2009, 08:58 AM
  3. Prove that...(using Binomial theorem)?
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 10th 2009, 06:42 PM
  4. Prove using Binomial and DeMoivre's Theorem?
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: February 12th 2009, 11:18 AM
  5. Prove using Binomial Theorem?
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 12th 2009, 09:51 AM

Search Tags


/mathhelpforum @mathhelpforum