structural:reformatting, linguistic:voice_change, information:filtering
2

The definition of the binomial coefficients can be extended to the case where n {\displaystyle n} is real and k {\displaystyle k} is integer.

In particular, the following identity holds for any non-negative integer k {\displaystyle k}:

This shows up when expanding 1 + x {\displaystyle {\sqrt {1+x}}} into a power series using the Newton binomial series :