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Maclaurin series of an elementary function question

  1. Nov 2, 2013 #1
    The Maclaurin series expansion for ##(1+z)^\alpha## is as follows:

    $$(1+z)^\alpha = 1 + \sum_{n=0}^\infty \binom{\alpha}{n}z^n$$ with $$|z|<1$$

    What I don't understand is why is ##|z|<1##?
  2. jcsd
  3. Nov 2, 2013 #2


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    The series won't converge for α, unless α is a non-negative integer.
    The magnitude of the binomial coefficient -> 1 as n -> ∞.
    Last edited: Nov 2, 2013
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