PlanetMath: Pascal's rule

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Pascal's rule

(Theorem)

Pascal's rule is the binomial identity

$\displaystyle \binom{n}{k} + \binom{n}{k-1} = \binom{n+1}{k}$

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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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

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Cross-references: binomial coefficient, identity, binomial
There are 13 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 9251 times total.

Classification:

05A19 (Combinatorics :: Enumerative combinatorics :: Combinatorial identities)

Pending Errata and Addenda

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