Results 1 to 13 of 13

Math Help - Binomial Expansion help.

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    6

    Binomial Expansion help.

    Hey,

    The question is:

    For the binomial expansion of ascending powers of x of (1+1/4x)^n, when n is an integer and n is bigger than 2.

    Find and simplify the first three terms.

    I got it to be 1+1/4x+(1/4x)^2

    But the answers are something different.

    Any idea what Im doing wrong?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Apr 2010
    Posts
    12
    Pascals Triangle should help....

    For n=2,

    1+2/4x+(1/16)x^2

    Because it is 2 * 1/4

    (a+b)^2 = a^2 + 2ab + b^2



    BUT, n is bigger than 2, so it should be...

    n = 3
    (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

    Pascal's Triangle is the one for probability, but those numbers also work for binomial expansions.

    Good luck.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2010
    Posts
    6
    When its n is bigger than 2 I dont think you can assign n as 3 it has to be n. If that makes sense?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    \left( {a + b} \right)^n  = \sum\limits_{k = 0}^n {\binom{n}{k}a^k b^{n - k} }
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2010
    Posts
    12
    Oh, no, I meant it as an example.

    So, looking at pascal's triangle for n = 4 (the fourth row), what is the expansion?

    I think that what is being said above me is waaay to complicated for you, but is saying that you do the sum of the Combinations nCr for the numbers you are given, and that is Pascal's triangle.


    Read a short article on it, the basics at least, to understand the expansion with ease.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Apr 2010
    Posts
    6
    I do understand what your saying and I have learnt about pascals triangle and using the nCp key but what I was hoping for was if someone were to attempt the question and show me where I have gone wrong.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    ^nC_k=\binom{n}{k}.
    (x+y)^6=\binom{6}{0}x^{6}y^{0}+\binom{6}{1}x^{5}y^  {1}+\binom{6}{2}x^{4}y^{2}+\binom{6}{3}x^{3}y^{3}+  \binom{6}{4}x^{2}y^{4}+\binom{6}{5}x^{1}y^{5}+\bin  om{6}{6}x^{0}y^{6}
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Apr 2010
    Posts
    6
    I understand that Plato, but it doesn't really help.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    Quote Originally Posted by jamesg007 View Post
    I understand that Plato, but it doesn't really help.
    Then what in the world are you asking?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Apr 2010
    Posts
    6
    Try reading my first post.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by jamesg007 View Post
    Try reading my first post.
    Why would you want to use Pascal's triangle to find the coefficients for? It is grossly inefficient to use it for high powers of n.

    You can also use the formula

    (1+x)^n = 1+nx + \frac{n(n-1)}{2!}x^2 + \frac{n(n-1)(n-2)}{3!}x^3  + \frac{n(n-1)(n-2)(n-3)}{4!}x^4 + ... + \frac{n!}{n!}x^n

    The coefficients of k are {n\choose k} = \frac{n!}{(n-k)!k!}
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Newbie
    Joined
    Apr 2010
    Posts
    6
    Thanks
    Follow Math Help Forum on Facebook and Google+

  13. #13
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by jamesg007 View Post
    Im not the one advocating the use of Pascals triangle.
    My apologies

    \left(1+ \frac{1}{4x}\right)^n

    You can use the formula in my last post but where x = \frac{1}{4x} in this case
    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, 10:55 AM
  2. [SOLVED] Binomial expansion
    Posted in the Algebra Forum
    Replies: 14
    Last Post: October 17th 2010, 10:45 AM
  3. Binomial expansion help
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 3rd 2009, 07:35 AM
  4. Replies: 6
    Last Post: May 1st 2009, 12:37 PM
  5. Binomial Expansion?
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 15th 2009, 03:35 PM

Search Tags


/mathhelpforum @mathhelpforum