1. Not finding help here? Sign up for a free 30min 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 representation of 1/(x+1)^2

  1. Feb 16, 2013 #1
    1. The problem statement, all variables and given/known data
    Use differentiation to find a power series representation for
    f(x)=1/(1+x)2


    2. Relevant equations


    3. The attempt at a solution

    1/(1-x) = [itex]\sum[/itex](x)n
    1/(1-(-x)) = [itex]\sum[/itex](-x)n

    Deriving 1/(1-(-x))
    -1/(1-(-x))2= [itex]\sum[/itex]n(-x)n-1 from n=1 to infinity

    indexing it from n=0,
    [itex]\sum[/itex](n+1)(-x)n

    finally,

    (-1)*-1/(1-(-x))2 = -[itex]\sum[/itex](n+1)(-x)n

    However, in the book, the answer is [itex]\sum[/itex](n+1)(-x)n. What am I forgetting? Thank you.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 16, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Check the derivative of (-x)^n again. Don't forget the chain rule.
     
  4. Feb 16, 2013 #3

    rock.freak667

    User Avatar
    Homework Helper

    When you differentiated (-x)^n, you forgot to multiply by -1.
     
  5. Feb 16, 2013 #4
    ooooooh. thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Series representation of 1/(x+1)^2
Loading...