Results 1 to 5 of 5

Math Help - Binomial Theorem

  1. #1
    Super Member
    Joined
    Dec 2009
    Posts
    755

    Binomial Theorem

    Given that (1+y)^8=1+8y+28y^2+56y^3+...

    In the expansion of (1+x+kx^2)^8 in ascending powers of x, the coefficient of y^3 is zero. Find the value of the constant k.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2010
    Posts
    715
    Thanks
    2
    Quote Originally Posted by Punch View Post
    Given that (1+y)^8=1+8y+28y^2+56y^3+...

    In the expansion of (1+x+kx^2)^8 in ascending powers of x, the coefficient of y^3 is zero. Find the value of the constant k.
    Put  y = x+kx^2 in the first identity we have \displaystyle (1+x+kx^2)^8=1+8(x+kx^2)+28(x+kx^2)^2+56(x+kx^2)^3  +...
    To have the coefficient of y^3 be zero, we must have 56(x+kx^2)^3 = 0 \Rightarrow x+kx^2 = 0  \Rightarrow x(1+kx) = 0 \Rightarrow k = -\frac{1}{x}.
    Last edited by TheCoffeeMachine; October 2nd 2010 at 09:25 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Dec 2009
    Posts
    755
    However, the answer is k=-1! and from the second sentence of the question, the expression doesn't contain y, where is there a coeff of y?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Mar 2010
    Posts
    715
    Thanks
    2
    Quote Originally Posted by Punch View Post
    However, the answer is k=-1! and from the second sentence of the question, the expression doesn't contain y, where is there a coeff of y?
    I thought they were asking you to consider y as x+kx^2 in the expansion  \sum_{r=0}^{8}\binom{8}{r}{y}^r to find k given that \binom{8}{3}(x+kx^2)^3 = 0,
    but it seems not. It's more likely that by the coefficient of y^3 they rather meant the coefficient of x^3, which gives k as indeed -1.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Dec 2009
    Posts
    755
    This question is weird. Surprisingly, it is a question from past years o levels paper!!! is there a problem with this question then?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Binomial Theorem
    Posted in the Statistics Forum
    Replies: 3
    Last Post: January 5th 2012, 04:44 PM
  2. Binomial Theorem.
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 12th 2010, 09:42 PM
  3. Binomial Theorem or Binomial Coefficient
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: October 2nd 2009, 02:06 PM
  4. Binomial Theorem:-
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: September 12th 2009, 01:19 AM
  5. Binomial Theorem
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 18th 2008, 06:29 AM

Search Tags


/mathhelpforum @mathhelpforum