Maclaurin series of an elementary function question

[Crake]

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 $|z|<1$?

 

[mathman]

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