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Math Help - Can you do it?

  1. #1
    Senior Member
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    Can you do it?

    Can you cook up a power series whose interval of convergence is the interval (0,
    1]?How about (0, infinity)? Give an explicit series or explain

    why you can't.

    thanks
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  2. #2
    MHF Contributor Calculus26's Avatar
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    for the first consder the power series representation of ln(x+1)

    If your studies haven't got you this far look in the taylor series section.

    For the second I'll give you a hint -- consider the radius of convergence
    for a power series (0,inf) where would the power series be centered?
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  3. #3
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    So the first one is (-1)^n+1*x^n/(n) and the second is impossible since you couldn't tell where it would be centered?
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  4. #4
    MHF Contributor Calculus26's Avatar
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    yes on the first one

    On the second If the radius of conv is inf the IC is (-inf,inf)

    Since inf/2 = inf you can't have have IC (0,inf)
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