- #1

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

What I don't understand is why is ##|z|<1##?

- Thread starter Crake
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- #1

- 64

- 1

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

What I don't understand is why is ##|z|<1##?

- #2

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 -> ∞.

The magnitude of the binomial coefficient -> 1 as n -> ∞.

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