Results 1 to 3 of 3

Math Help - [SOLVED] combination prove ques

  1. #1
    mathG
    Guest

    [SOLVED] combination prove ques

    ( The better form of the question with correct symbols is here.
    http://www.geocities.com/johntyung/Q2.pdf )


    *** For this problem I heard that they solved it by just using the identity and manipulating it algebraically. Without using induction. ***

    for n even, prove that

    (n choose 0) + (n choose 2) + (n choose 4) +...+ (n choose n)=2^(n-1)

    and

    (n choose 1) + (n choose 3) +...+(n choose (n-1)) = 2^(n-1)

    using mathematical induction and/or various identities involving binomial coefficients.
    (Hint: first establish the identity,

    ((m+2) choose k) = (m choose k)+ 2(m choose (k-1)) +(m choose (k-2) )

    Then, when doing the induction, do a simultaneous induction on both identities.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    hpe
    hpe is offline
    Member hpe's Avatar
    Joined
    Apr 2005
    Posts
    158
    This is too complicated. Prove that

    nC0 + nC1 + nC2 + nC3 + ... + nCn = 2^n

    and

    nC0 - nC1 + nC2 - nC3 + ... + nCn = 0 (assuming n is even).

    Then add and subtract these two identities. They follow from 1+1 = 2 and 1-1 = 0 and the Binomial Theorem.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2005
    Posts
    35
    Looks like a binomial series with a and b equal to 1, http://tutorial.math.lamar.edu/AllBr...mialSeries.asp
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Linear combination of a vector S
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 27th 2010, 10:47 AM
  2. [SOLVED] Probability involving Combination
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 30th 2009, 04:04 PM
  3. [SOLVED] Permutation and Combination Question 1
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: February 8th 2009, 10:08 AM
  4. combination problem [SOLVED]
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: October 29th 2008, 10:55 PM
  5. [SOLVED] Combination/probability help please
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 12th 2007, 02:34 PM

Search Tags


/mathhelpforum @mathhelpforum