The Sum

Algebra Level 3

The sum i=12013(1)i1i=112+1314+12012+12013\sum\limits_{i=1}^{2013} \frac{\left(-1\right)^{i-1}}{i} = 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \cdots - \frac{1}{2012} + \frac{1}{2013} equals ____________.\text{\_\_\_\_\_\_\_\_\_\_\_\_}.

SOURCE: NSEJS 2013

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