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Power series question

  1. Apr 4, 2004 #1
    the question is can you come up with a power series whose interval of convergance is the interval (0,1] that is 0 < x < = 1 ? how about (0,infinity)? Give an explicit series of explain why you can't.

    The first part of this question where they ask if a series can have an interval of (0,1). I dont think such a series can exist becaue when x=0 doesnt the series always converge, there for the series would have to be eqal to 0. so it can have an interval of [0,1) but not (0,1). but that would also mean a series can't have an interval of (0,infinity).

    i just wan to know if it i am going the right way in my thinking and if, not if some one could point me in the right direction.

  2. jcsd
  3. Apr 4, 2004 #2


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    Power series don't have to be in x; they can be in (x - a) for some a...
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