Mathematics-Online lexicon: Pascal's Triangle

	[home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff]
	Mathematics-Online lexicon:
	Pascal's Triangle

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

overview

The binomial coefficients

$\displaystyle \binom{n}{k} = \frac{n!}{(n-k)!\,k!}$

can be recursively calculated by

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

The recursion, known as Pascal's triangle, is illustrated in the figure.

$\begin{center} \begin{tabular}{c\vert cccccccccccccc} $\displaystyle \binom{0}{k... ...dots$\ & & $\vdots$\ & & $\vdots$\ & & $\vdots$\ & \\ \end{tabular}\end{center}$

(Authors: Höllig/Knesch/Abele)

Annotation:

Proof of the Binomial Recursion

[Links]

automatically generated 6/11/2007