Maclaurin series of an elementary function question

  • Thread starter Crake
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  • #1
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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##?
 

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  • #2
mathman
Science Advisor
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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 -> ∞.
 
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