1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Series expansion/algebra problem

  1. Apr 26, 2014 #1
    Hi,

    i'm revising series expansions and my problem has arisen from an example in my text book, but it's not directly related to the series expansion itself. It's more of an algebra question, where they've made a rearrangement I can't follow...

    1. The problem statement, all variables and given/known data

    If [itex]n[/itex] is a positive integer find the coefficient of [itex]x^{r}[/itex] in the expansion of [itex](1 + x)(1 - x)^{n}[/itex] as a series of ascending powers of x.

    2. Relevant equations



    3. The attempt at a solution

    The solution starts by stating the following expressions are equivalent.

    [itex](1 + x)(1 - x)^{n} \equiv (1 - x)^{n} + x(1 - x)^{n}[/itex]

    If I take this statement to be true, I can follow through the rest of the example without a hitch, but I just can't see what they've done here.

    Thanks for any help you can give,

    BOAS.
     
  2. jcsd
  3. Apr 26, 2014 #2
    Let ##(1-x)^n=a##, then ##a(1+x)=a+ax##. Do you see now? :)
     
  4. Apr 26, 2014 #3
    Perfectly.

    Thank you!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Series expansion/algebra problem
Loading...