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Contests
National and Regional Contests
Russia Contests
Russian Team Selection Tests
Russian TST 2016
P2
Inequality with powers of two
Inequality with powers of two
Source: Russian TST 2016, Day 11 P2 (Group A), P3 (Group B)
April 19, 2023
algebra
inequalities
Problem Statement
Prove that
1
+
2
1
1
−
2
1
+
2
2
(
1
−
2
1
)
(
1
−
2
2
)
+
⋯
+
2
2016
(
1
−
2
1
)
⋯
(
1
−
2
2016
)
>
0.
1+\frac{2^1}{1-2^1}+\frac{2^2}{(1-2^1)(1-2^2)}+\cdots+\frac{2^{2016}}{(1-2^1)\cdots(1-2^{2016})}>0.
1
+
1
−
2
1
2
1
+
(
1
−
2
1
)
(
1
−
2
2
)
2
2
+
⋯
+
(
1
−
2
1
)
⋯
(
1
−
2
2016
)
2
2016
>
0.
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