- #1

- 68

- 0

## Homework Statement

Ok, I know that [tex] (-1)^r \binom {n} {r} [/tex] is supposed to equal 0. But I have plugged some numbers into this series, and this doesn't seem to be true for even numbers of n? Like for n = 4 and r = 4, I have:

[tex] 1 - \frac{4!}{1!3!} + \frac{4!}{2!2!} - \frac{4!}{3!1!} + \frac{4!}{4!} [/tex]. The [tex] \frac{4!}{2!2!} [/tex] seems to be in the way. For even numbers, the [tex]\frac{n!}{(n/2)!(n/2)!}[/tex] does not seem to cancel out, resulting in the series not being equal to zero. Am I doing something wrong at [tex]\frac{n!}{(n/2)!(n/2)!}[/tex]?

## Homework Equations

[tex] 1 - \binom {n} {1} + \binom {n} {2} - \binom {n} {3} + \cdots + (-1)^r \binom {n} {n} = 0[/tex]

## The Attempt at a Solution

See #1.