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# Pascal’s rule

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.

Keywords:

number theory combinatorics

Related:

BinomialCoefficient, VandermondeIdentity, PascalsTriangle, TheoremOfThePrimalRay, Mm2, Mm, LeTheoremeDuRayonPrimal, LeDeuxiemeTheoremeDuRayonPrimal, AProofOfGoldbachConjecture, AProofOfDePolignacConjectures, FermatGhanouchiSeriesAmazingFermatGhanouchiSequ

Type of Math Object:

Theorem

Major Section:

Reference

## Mathematics Subject Classification

05A19*no label found*

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## Recent Activity

Apr 15

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz

Mar 26

new correction: Misspelled name by DavidSteinsaltz

Mar 21

new correction: underline-typo by Filipe

Mar 19

new correction: cocycle pro cocyle by pahio

Mar 7

new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier

new image: expected waiting time by robert_dodier

new image: plot W(t) = P(waiting time <= t) by robert_dodier

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz

Mar 26

new correction: Misspelled name by DavidSteinsaltz

Mar 21

new correction: underline-typo by Filipe

Mar 19

new correction: cocycle pro cocyle by pahio

Mar 7

new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier

new image: expected waiting time by robert_dodier

new image: plot W(t) = P(waiting time <= t) by robert_dodier