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Interval of Convergence of Power Series with Square Root

  1. Apr 25, 2016 #1
    I'm trying to find the answer to a question similar to this posted it earlier but in the wrong section I think and not explained well.
    $$
    \sum_{{\rm n}=0}^\infty \left (-\sqrt x \right )^n \ \ \rm ?$$
    Find the interval of convergence?
    I tried using the root test and got from 0 to 1 but when I checked with Wolfram and it gave from -1 to 1 saying the absolute value would go inside the square root. Am I doing something wrong or is Wolfram making a mistake. Thanks in advance for any help.
     
  2. jcsd
  3. Apr 25, 2016 #2

    LCKurtz

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    Assuming ##x## is real, ##x<0## is not in the domain.
     
  4. Apr 25, 2016 #3
    Thank you for the help in clearing up my confusion.
     
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