2014 UNCO Math Contest II Problems/Problem 2

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Problem

Define the Cheshire Cat function $\fbox{:)}$ by

\begin{align*}  \fbox{:)}(x) &= -x \quad \text {if } x \text{ is even and} \\ \fbox{:)}(x) &= x \quad \text{ if  }x \text{ is odd}  \end{align*}

Find the sum $\fbox{:)}(1) + \fbox{:)}(2) + \fbox{:)}(3) + \fbox{:)}(4) + . . .+ \fbox{:)}(289)$


Solution

See also