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Regional Mathematical Olympiad
1998 India Regional Mathematical Olympiad
3
An ineq - simple
An ineq - simple
Source: Indian RMO 1998 Problem 3
October 26, 2005
inequalities
Problem Statement
Prove that for every natural number
n
>
1
n > 1
n
>
1
1
n
+
1
(
1
+
1
3
+
1
5
+
…
+
1
2
n
−
1
)
>
1
n
(
1
2
+
1
4
+
…
+
1
2
n
)
.
\frac{1}{n+1} \left( 1 + \frac{1}{3} +\frac{1}{5} + \ldots + \frac{1}{2n-1} \right) > \frac{1}{n} \left( \frac{1}{2} + \frac{1}{4} + \ldots + \frac{1}{2n} \right) .
n
+
1
1
(
1
+
3
1
+
5
1
+
…
+
2
n
−
1
1
)
>
n
1
(
2
1
+
4
1
+
…
+
2
n
1
)
.
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