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The sum ∑i=12013(−1)i−1i=1−12+13−14+⋯−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}i=1∑2013i(−1)i−1=1−21+31−41+⋯−20121+20131 equals ____________.\text{\_\_\_\_\_\_\_\_\_\_\_\_}.____________.
SOURCE: NSEJS 2013
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The sum i=1∑2013i(−1)i−1=1−21+31−41+⋯−20121+20131 equals ____________.