Results 1 to 2 of 2

Math Help - General formula for the expansion of binomials with non-integer indices

  1. #1
    Newbie
    Joined
    Apr 2011
    Posts
    12

    General formula for the expansion of binomials with non-integer indices

    I'm familiar with binomial expansions in the form of (a+b)^n, where n is an integer. However, today I came across the following:
    \sqrt[3]{1+\frac{1}{n^3}} \:=\: 1+\frac{1}{3n^3}+\frac{1}{9n^6}+\frac{5}{81n^9} + \ldots

    How is that result reached? Is there a general expression for the expansion of (a+b)^n where n is not an integer?

    (I searched online, but I didn't find anything that explained what I was after.)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,315
    Thanks
    1223
    Search for Newton's Generalised Binomial Series.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: March 5th 2010, 03:11 AM
  2. Expansion of a rotation-formula
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 14th 2010, 12:45 PM
  3. Expansion of Binomials???
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 15th 2009, 11:14 PM
  4. Rodrigues Formula expansion
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 24th 2008, 08:55 AM
  5. Expansion of taylor's formula in 3 variables?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: December 24th 2007, 09:03 AM

Search Tags


/mathhelpforum @mathhelpforum