Sum over k of -2 Choose k

Theorem

 * $\displaystyle \sum_{k \mathop = 0}^n \binom {-2} k = \left({-1}\right)^n \left\lceil {\dfrac {n + 1} 2}\right\rceil$

where:
 * $\dbinom {-2} k$ is a binomial coefficient
 * $\left\lceil {x}\right\rceil$ denotes the ceiling of $x$.