Truncated Binomial Series

Can the truncated binomial series be expressed as a closed form \begin{align} \sum_{k=0}^{\lfloor (n-1)/2 \rfloor} \binom{n}{k} x^{k} \end{align}

• It can be expressed in terms of the Hypergeometric function. – Marco Cantarini Mar 16 '15 at 6:16
• I believe there is a simpler form. – science Mar 16 '15 at 6:34