- #1

- 25

- 0

how do I evaluate [tex] \sum_{k=0}^d \binom{n+d-k}{n} [/tex] ?

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- Thread starter mathstime
- Start date

- #1

- 25

- 0

how do I evaluate [tex] \sum_{k=0}^d \binom{n+d-k}{n} [/tex] ?

- #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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