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- Feb 14, 2012
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Let \(\displaystyle X=\frac{1}{1\cdot2}+\frac{1}{3\cdot4}+\cdots+\frac{1}{2011\cdot2012}\) and \(\displaystyle Y=\frac{1}{1007\cdot2012}+\frac{1}{1008\cdot2011}+\cdots+\frac{1}{2012\cdot1007}\).
Evaluate \(\displaystyle \frac{X}{Y}\).
Evaluate \(\displaystyle \frac{X}{Y}\).