Summation combinatorics

  • Thread starter mathstime
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  • #1
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how do I evaluate [tex] \sum_{k=0}^d \binom{n+d-k}{n} [/tex] ?
 

Answers and Replies

  • #2
1,015
3


I don't know the method. But first you could change the variable of integration to [itex]k'=d-k[/itex] and then you look it up :)
I think the answer is
[tex]\binom{n+d+1}{d}[/tex]
 
  • #3
64
0


The answer is:
[tex]\left(
\begin{array}{c}
n+d+1 \\
n+1
\end{array}
\right)[/tex]

Please refer to:

http://www.voofie.com/content/76/evaluating-summation-involving-binomial-coefficients/" [Broken]

for the steps and how to deal with problem of this type.
 
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