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Mathematik-Online problems:

Problem 186: Summation Formulas for Binomial Coefficients

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
Prove the following equations and illustrate the solutions in Pascal's Triangle.
a) $ {\displaystyle{\sum_{k=0}^n \left(\begin{array}{c} m+k\\ k \end{array}\right) = \left(\begin{array}{c} m+n+1\\ n \end{array}\right)}}$          b) $ {\displaystyle{\sum_{\ell=1}^n \left(\begin{array}{c} n+k-\ell \\ k \end{array}\right) = \left(\begin{array}{c} n+k\\ k+1 \end{array}\right)}}$
(Authors: Höllig/Abele)
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  automatisch erstellt am 19.  4. 2006