Summation combinatorics

1. Mar 9, 2010

mathstime

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

2. Mar 9, 2010

Gerenuk

Re: summation/combinatorics

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 :)
$$\binom{n+d+1}{d}$$

3. Jun 15, 2010

ross_tang

Re: summation/combinatorics

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