# Factorial and summation.

1. Sep 25, 2007

### babyrudin

Hello all! In solving some math problems, I encountered the following sum:

$$\sum_{k=1}^{r+1} kb \frac{r!}{(r-k+1)!} \frac{(b+r-k)!}{(b+r)!}. \quad \mbox{(eqn.1)}$$

Now, I have asked Maple to calculate the above sum for me, and the answer takes a very simple form:

$$\frac{b+r+1}{b+1}. \quad \mbox{(eqn.2)}$$

My question is, does anyone know how to go from (eqn.1) to (eqn.2)? I am really bad at working with factorials, and so far I am not getting close. Maybe there are some results and properties of factorials and summation that can be used to simplify the above?

2. Sep 25, 2007

### EnumaElish

I suggest assuming specific values for b, r, k.