Choose alternatively

Algebra Level 3

Find k=02014(1)k(2014k)\displaystyle\sum_{k=0}^{2014}(-1)^k\left(\begin{matrix}2014\\k\end{matrix}\right), where (nr)=n!(nr)!r!\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 (20140)(20141)+(20142)(20143)+(20142013)+(20142014)\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)

×

Problem Loading...

Note Loading...

Set Loading...