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Math Help - interval of convergence

  1. #1
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    interval of convergence

    Let, f(x) = SUM n_infinity x^n/x^2

    find interval of convergence: f, f', and f"

    thanks for any help for this one.
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  2. #2
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    Quote Originally Posted by rcmango View Post
    Let, f(x) = SUM n_infinity x^n/x^2

    find interval of convergence: f, f', and f"

    thanks for any help for this one.
    This is not a power series.
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  3. #3
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    Quote Originally Posted by rcmango View Post
    Let, f(x) = SUM n_infinity x^n/x^2

    find interval of convergence: f, f', and f"

    thanks for any help for this one.
    f(x) = SUM_{n=1 to infty} [x^n/x^2] = sum_{x=1 to infty} x^{n-2}

    has a singularity at x=1 otherwise is convergent when |x|<1 when:

    sum_{x=1 to infty} x^{n-2} = 1/x + 1/(1-x) = 1/[x(1-x)]

    RonL
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