Problem for the next year!

Algebra Level 4

\[\large{\dfrac{ \displaystyle \frac{1}{1}-\frac{1}{2}+\frac{1}{3} - \frac{1}{4} + \ldots + \frac{1}{2015}-\frac{1}{2016} }{\displaystyle \frac{1}{1009}+\frac{1}{1010} + \frac{1}{1011} + \ldots + \frac{1}{2015}+\frac{1}{2016} } = \ ? }\]

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