Binomial Theorem :: Confusion with Wiki Entry

Question

I wanted an expansion of $(1+x)^n$ and refered Wikipedia but I don't understand why there is a condition of $|x|<1$.

In general, for the series, the condition is not required am I right or am I missing something subtle?

@AndréNicolas. Gotcha. Thanks! – Inquest Jan 19 '13 at 20:32 — Inquest, Jan 19 '13 at 20:32

score 2 · Accepted Answer · answered Jan 19 '13 at 20:32

For the ordinary Binomial Theorem, where $n$ is a non-negative integer, there is no $|x|\lt 1$ restriction. In the generalization of the ordinary Binomial Theorem to situations where $n$ is not necessarily a non-negative integer, you get an infinite series that only converges if $|x|\lt 1$.

Binomial Theorem :: Confusion with Wiki Entry

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