Difference between revisions of "Binomial coefficient"
From specialfunctionswiki
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The binomial coefficients are defined by the formula | The binomial coefficients are defined by the formula | ||
| − | $${n \choose k} = \dfrac{n!}{(n-k)!k!}.$$ | + | $${}_nC_k:={n \choose k} = \dfrac{n!}{(n-k)!k!}.$$ |
=Properties= | =Properties= | ||
Revision as of 05:23, 11 January 2015
The binomial coefficients are defined by the formula $${}_nC_k:={n \choose k} = \dfrac{n!}{(n-k)!k!}.$$
Properties
Theorem (Binomial Theorem): $(a+b)^n = \displaystyle\sum_{k=0}^n {n \choose k} a^k b^{n-k}$
Proof: █
