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Mathematics-Online lexicon: Annotation to

Pascal's Triangle


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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}


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  automatisch erstellt am 19.  8. 2013