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Math Help - differentiation and power series representation

  1. #1
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    differentiation and power series representation

    this was a very long problem. was confusing to jump back and forth, need help breaking this one down please.

    heres the questions and the problem:

    use differentiation to find a power series representation for f(x) 1/(1+x)^2

    what is the radius of convergence?

    b.) use part(a) to find a power series for f(x) = 1/(1+x)^3

    c.) use part (b) to find a power series for f(x) = x^2/(1+x)^3
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rcmango View Post
    this was a very long problem. was confusing to jump back and forth, need help breaking this one down please.

    heres the questions and the problem:

    use differentiation to find a power series representation for f(x) 1/(1+x)^2

    what is the radius of convergence?

    b.) use part(a) to find a power series for f(x) = 1/(1+x)^3

    c.) use part (b) to find a power series for f(x) = x^2/(1+x)^3
    Note that 1/(1 + x)^2 = - d/dx [1/(1 + x)]

    and you know the power series representation as TPH calculated it for you here

    turn his answer into a single expression (it would be SUM{n goes from 0 to infinity} (-1)^n *x^n) and differentiate that expression, and add a minus sign in front and you will have the answer for part (a). the other parts are similar.
    Last edited by Jhevon; April 19th 2007 at 08:51 PM.
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  3. #3
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    ya, theres alot going on in that problem. thanks for the help.
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