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Problems
Contests
National and Regional Contests
Russia Contests
Moscow Mathematical Olympiad
1950 Moscow Mathematical Olympiad
182
182
Part of
1950 Moscow Mathematical Olympiad
Problems
(1)
MMO 182 Moscow MO 1950 product 1/2 3/4 5/6 7/8 ... 99/100 <1/10
Source:
8/6/2019
Prove that
1
2
3
4
5
6
7
8
.
.
.
99
100
<
1
10
\frac{1}{2} \frac{3}{4} \frac{5}{6} \frac{7}{8} ... \frac{99}{100 } <\frac{1}{10}
2
1
4
3
6
5
8
7
...
100
99
<
10
1
.
algebra
inequalities
Product