Compare aa and bb

Algebra Level 5

a=112+1314+1516++1199912000b=11000+11001+11002++12000\begin{aligned} a&=& 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} - \frac{1}{6} + \cdots+ \frac{1}{1999}-\frac{1}{2000} \\ b&= &\frac{1}{1000} + \frac{1}{1001} + \frac{1}{1002} + \cdots + \frac{1}{2000} \end{aligned}

Which of the following is true?

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