Results 1 to 7 of 7

Math Help - Binomial Expansion(2)

  1. #1
    Super Member
    Joined
    Dec 2009
    Posts
    755

    Binomial Expansion(2)

    Find the coefficient of x^7 in the expansion of (2x^2+\frac{1}{x})^{11}

    I found r=7\frac{1}{3} and could not work with a fraction....

    Basically, I equated the powers of x to zero,

    2(11-r)-r=0

    and found r=7\frac{1}{3}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by Punch View Post
    Find the coefficient of x^7 in the expansion of (2x^2+\frac{1}{x})^{11}

    I found r=7\frac{1}{3} and could not work with a fraction....

    Basically, I equated the powers of x to zero,

    2(11-r)-r=0

    and found r=7\frac{1}{3}
    Sorry but what does r represent? It might help you to rewrite \frac{1}{x} as x^{-1}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2009
    Posts
    806
    Thanks
    4
    r cannot be a fraction.

    (x^2)^{(11-r)}(x)^{-1} = x^7

    22 - 3r = 7.

    Now find r.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Aug 2010
    Posts
    1
    you can't get r in fraction, it has to be a natural number.
    With that you'll get
    => 22-3r = 7
    => 22-7 = 3r
    => 15 = 3r
    => 5 = r
    Last edited by mr fantastic; August 7th 2010 at 02:37 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Dec 2009
    Posts
    755
    I realised that I equated it to 0, thinking that it was an independent term...

    However, what if the questions ask for an independent term, would it be possible?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Sep 2008
    From
    West Malaysia
    Posts
    1,261
    Quote Originally Posted by Punch View Post
    I realised that I equated it to 0, thinking that it was an independent term...

    However, what if the questions ask for an independent term, would it be possible?
    yes in that case.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1
    If it easy for you, we can look at: (2x^2+1/x)11={1/x^11}{2x^3+1)^11, notice that now we need to find the coefficient x^18 of {2x^3+1)^11...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Binomial expansion
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: June 26th 2011, 09:55 AM
  2. [SOLVED] Binomial expansion
    Posted in the Algebra Forum
    Replies: 14
    Last Post: October 17th 2010, 09:45 AM
  3. Binomial expansion help
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 3rd 2009, 06:35 AM
  4. Replies: 6
    Last Post: May 1st 2009, 11:37 AM
  5. Binomial Expansion?
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 15th 2009, 02:35 PM

Search Tags


/mathhelpforum @mathhelpforum