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MMO 182 Moscow MO 1950 product 1/2 3/4 5/6 7/8 ... 99/100 <1/10

Source:

August 6, 2019

algebrainequalitiesProduct

Problem Statement

Prove that

\frac{1}{2} \frac{3}{4} \frac{5}{6} \frac{7}{8} ... \frac{99}{100 } <\frac{1}{10}