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Algebra
Level
3
Find \(\displaystyle\sum_{k=0}^{2014}(-1)^k\left(\begin{matrix}2014\\k\end{matrix}\right)\), where \(\displaystyle\left(\begin{matrix}n\\r\end{matrix}\right)=\frac{n!}{(n-r)!r!}\) denotes combination.
For those of you who do not comprehend \(\sum\), find \(\left(\begin{matrix}2014\\0\end{matrix}\right)-\left(\begin{matrix}2014\\1\end{matrix}\right)+\left(\begin{matrix}2014\\2\end{matrix}\right)-\left(\begin{matrix}2014\\3\end{matrix}\right)+\cdots-\left(\begin{matrix}2014\\2013\end{matrix}\right)+\left(\begin{matrix}2014\\2014\end{matrix}\right)\)
by
Kenny Lau