# Homework Help: Binomial Series Question

1. Oct 6, 2006

How does one deduce the following:

We are given

$$\binom{-3}{n} = \frac{(-3)(-4)(-5)\cdot\cdot\cdot\cdot\cdot(-3-n+1)}{n!} = \frac{(-3)(-4)(-5)\cdot\cdot\cdot\cdot[-(n+2)]}{n!}$$. How do we get from here to:

$$\frac{(-1)^{n}\cdot2\cdot3\cdot4\cdot5\cdot\cdot\cdot\cdot(n+1)(n+2)}{2\cdot n!} = \frac{(-1)^{n}(n+1)(n+2)}{2}$$?

Thanks

Last edited: Oct 6, 2006
2. Oct 6, 2006