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Prove sum

Source: Baltic Way 1995

October 8, 2011

inductionlogarithmsalgebra proposedalgebra

Problem Statement

Prove that

\frac{1995}{2}-\frac{1994}{3}+\frac{1993}{4}-\ldots -\frac{2}{1995}+\frac{1}{1996}=\frac{1}{999}+\frac{3}{1000}+\ldots +\frac{1995}{1996}