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Powe series of functions

  1. Jul 7, 2003 #1


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    Hi, I am stuck on this problem!

    Given the function, find the first four terms of the power series representation and find the domain of convergence?

    function is;

    my calculation;
    find derivatives of the function.


    I am having difficulty in knowing if what I did was correct.

    I'm not sure if this is how you are meant to approach it and if what I did was the correct way to go about solving the problem.

    If anyone can help me in solving my problem your help will be appreciated.

  2. jcsd
  3. Jul 8, 2003 #2
    Hi dan,
    I think you should use Taylor's formula.
    It's true you need the derivatives.
    But I think your results are wrong. I get, for instance,

  4. Jul 8, 2003 #3


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    Use the binomial expansion to get a series for (1-2x)-3, multiply the first few terms by (1-x). It will converge for |x|<1/2.
  5. Jul 9, 2003 #4
    Your derivatives are not exactly correct. You need to use the quotient rule and the chain rule in this case.
    Remember the quotient rule y' = (vu' - uv')/v^2.
    Now let u = (1-x) and v = (1-2x)^3.
    u' = -1, v' = -6(1-2x)^2 (chain rule).

    therefore y' = (-(1-2x)^3-(-6)(1-x)(1-2x)^2)/(1-2x)^6
    = ((1-2x)^2(5-4x))/(1-2x)^6
    = (5-4x)/(1-2x)^4
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