Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag
Mathematics-Online course: Basic Mathematics - Combinatorics

Pascal's Triangle

[previous page] [next page] [table of contents][page 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)

(temporary unavailable)
[previous page] [next page] [table of contents][page overview]
  automatically generated 10/31/2008