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Pascal's rule (Theorem)

Pascal's rule is the binomial identity $$ \binom{n}{k} + \binom{n}{k-1} = \binom{n+1}{k} $$ where $1 \leq k \leq n$ and $\binom{n}{k}$ is the binomial coefficient.




"Pascal's rule" is owned by KimJ.
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See Also: binomial coefficient, Vandermonde identity, Pascal's triangle

Keywords:  number theory combinatorics

Attachments:
Pascal's rule proof (Proof) by akrowne
Pascal's rule (bit string proof) (Proof) by vampyr
proof of Pascal's rule (Proof) by drini
Pascal's triangle is symmetrical along its central column (Corollary) by PrimeFan
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Cross-references: binomial coefficient, identity, binomial
There are 14 references to this entry.

This is version 5 of Pascal's rule, born on 2001-10-16, modified 2002-11-07.
Object id is 246, canonical name is PascalsRule.
Accessed 11303 times total.

Classification:
AMS MSC05A19 (Combinatorics :: Enumerative combinatorics :: Combinatorial identities)

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