## Quick Reference

The coefficient of a power of *x* in the binomial expansion of (1+*x*)* ^{n}*. The general binomial coefficient is defined, for any value of

*n*and for any positive integer

*r*, by . By convention, . Suppose now that

*n*is a non-negative integer. In this case is an integer and . Furthermore,. If

*r*≤

*n*then is also written as

^{n}*C*

*(*

_{r}*see*combination) and . The phrase ‘binomial coefficient’ appears in English in a mathematics text of 1876.

*Subjects:*
Mathematics.