How Do I Evaluate a Summation Involving Binomial Coefficients?

[mathstime]

how do I evaluate $$\sum_{k=0}^d \binom{n+d-k}{n}$$ ?

 

[Gerenuk]

I don't know the method. But first you could change the variable of integration to $k'=d-k$ and then you look it up :)
I think the answer is
$$\binom{n+d+1}{d}$$

 

[ross_tang]

The answer is:
$$\left( \begin{array}{c} n+d+1 \\ n+1 \end{array} \right)$$

Please refer to:

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

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