Results 1 to 2 of 2

Math Help - Binomial series

  1. #1
    Member
    Joined
    Dec 2007
    Posts
    90

    Binomial series

    Expand
    (1+2x) ^(5/2)


    So far i have

    1 + 5x 15/2 x but am not sure about the x

    thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,453
    Thanks
    1868
    Quote Originally Posted by gracey View Post
    Expand
    (1+2x) ^(5/2)


    So far i have

    1 + 5x – 15/2 x but am not sure about the x

    thanks
    The generalized binomial formula (a+ b)^c where c does not have to be an integer says
    (a+ b)^c= \sum_{n=0}^\infty \left(\begin{array}{c}c \\ n\end{array}\right) x^n y^{c-n}
    where, with c not an integer, we interpret \left(\begin{array}{c}c \\ n\end{array}\right) as \frac{c(c-1)(c-2)\cdot\cdot\cdot(c-n+1)}{n!}, for n= 0, 1 for n= 0.

    In this case, with c= 5/2, \left(\begin{array}{c}5/2 \\ 0 \end{array}\right)= 1, so the x^0 term is 1, \left(\begin{array}{c}5/2 \\ 1\end{array}\right)= 5/2 so the "x" term is (5/2)(2x)= 5/2 x as you say. \left(\begin{array}{c}5/2 \\ 2\end{array}\right)= ((5/2)(3/2)/2)(2x)^2= (15/2)x^2 as you say. \left(\begin{array}{c}5/2 \\ 3\end{array}\right)= ((5/2)(3/2)(1/2)/6)(4x)^3= [(15/8)/6](64x^3)= 20x^3
    Check my arithmetic!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Binomial Series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 16th 2010, 05:26 AM
  2. Binomial series?
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 11th 2009, 07:40 PM
  3. Binomial Series to find a Maclaurin Series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 21st 2009, 08:15 AM
  4. binomial series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 22nd 2008, 12:31 PM
  5. Binomial Series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 14th 2008, 02:23 PM

Search Tags


/mathhelpforum @mathhelpforum