Results 1 to 7 of 7

Math Help - Difficult problem involving factorials and binomial expansion. Can anyone help me?

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    3

    Difficult problem involving factorials and binomial expansion. Can anyone help me?

    Given that n is a positive integer and that a and b are real constants, find a and bi if :

    (1+ax)^n=1-6x+(81/5)x^2+bx^3+.

    Hint: You must solve for n first

    A step by step explanation would be greatly appreciated. This question really has me stumped and the teacher's explanation didn't help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    311
    Thanks
    2
    Ok I'll help you through it.
    Write down the first few terms of (1+ax)^n
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2010
    Posts
    3
    Okay. I think this is what you mean.

    1-6x+(81/5)x^2+bx^3+............
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by mm19 View Post
    Okay. I think this is what you mean.

    1-6x+(81/5)x^2+bx^3+............
    All you have done is written out the right hand side! Exactly how do you think that will help? You were told to "Write down the first few terms of (1+ax)^n" - with the expectation that you would do so by expanding it using the binomial theorem!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2010
    Posts
    3
    Sorry I got confused on what he meant.

    nC1 (1)^(n-1) (ax)^1
    nC2 (1)^(n-2) (ax)^2
    nC3 (1)^(n-3) (ax)^3

    I'm assuming this is what he means.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by mm19 View Post
    Sorry I got confused on what he meant.

    nC1 (1)^(n-1) (ax)^1
    nC2 (1)^(n-2) (ax)^2
    nC3 (1)^(n-3) (ax)^3

    I'm assuming this is what he means.
    What about the "r = 0" term?

    Now what you do is equate the coefficients of powers of x on each side of the expression given in the question and draw a conclusion.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    311
    Thanks
    2
    To mm19....."she" means not "he" means!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Problem involving factorials and "choosing"
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 8th 2011, 02:47 PM
  2. [SOLVED] Binomial expansion problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 22nd 2010, 01:41 PM
  3. Binomial expansion problem
    Posted in the Algebra Forum
    Replies: 0
    Last Post: February 15th 2010, 09:43 AM
  4. Replies: 3
    Last Post: February 14th 2009, 08:35 PM
  5. Binomial Expansion Problem - Please help!
    Posted in the Algebra Forum
    Replies: 5
    Last Post: May 28th 2008, 06:06 AM

Search Tags


/mathhelpforum @mathhelpforum