Difference between revisions of "Binomial coefficient"
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=Properties= | =Properties= | ||
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[[Binomial theorem]] | [[Binomial theorem]] | ||
| + | [[Binomial coefficient (n choose k) equals (n choose (n-k))]]<br /> | ||
| + | [[Binomial coefficient (n choose k) equals (-1)^k ((k-n-1) choose k)]]<br /> | ||
| + | [[Binomial coefficient ((n+1) choose k) equals (n choose k) + (n choose (k-1))]]<br /> | ||
| + | [[Binomial coefficient (n choose 0) equals 1]]<br /> | ||
| + | [[Binomial coefficient (n choose n) equals 1]]<br /> | ||
| + | [[Sum over bottom of binomial coefficient with top fixed equals 2^n]]<br /> | ||
| + | [[Alternating sum over bottom of binomial coefficient with top fixed equals 0]]<br /> | ||
=Videos= | =Videos= | ||
Revision as of 02:57, 4 June 2016
The binomial coefficients are defined by the formula $${}_nC_k:={n \choose k} = \dfrac{n!}{(n-k)!k!}.$$
Graph of the complex binomial coefficient function.
Properties
Binomial theorem
Binomial coefficient (n choose k) equals (n choose (n-k))
Binomial coefficient (n choose k) equals (-1)^k ((k-n-1) choose k)
Binomial coefficient ((n+1) choose k) equals (n choose k) + (n choose (k-1))
Binomial coefficient (n choose 0) equals 1
Binomial coefficient (n choose n) equals 1
Sum over bottom of binomial coefficient with top fixed equals 2^n
Alternating sum over bottom of binomial coefficient with top fixed equals 0
Videos
Pascal's Triangle and the Binomial Coefficients
Example of choose function (Binomial Coefficient)
Binomial coefficients
