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- Feb 14, 2012

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I have been trying so hard to prove the following:

\(\displaystyle \frac{1989}{2}-\frac{1988}{3}+\frac{1987}{4}-\cdots-\frac{2}{1989}+\frac{1}{1990}=\frac{1}{996}+\frac{3}{997}+\frac{5}{998}+\cdots++\frac{1989}{1990}\)

but to no avail and what I couldn't bear was that my approach gave me a tremendously messy bundle of terms everywhere on the paper...

Could you please at least give me some idea on how to prove it?

Thanks in advance.