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Regional Mathematical Olympiad
2002 India Regional Mathematical Olympiad
6
Simple inequality
Simple inequality
Source: Indian RMO 2002 Problem 6
October 27, 2005
inequalities
limit
Problem Statement
Prove that for any natural number
n
>
1
n > 1
n
>
1
,
1
2
<
1
n
2
+
1
+
2
n
2
+
2
+
…
+
n
n
2
+
n
<
1
2
+
1
2
n
.
\frac{1}{2} < \frac{1}{n^2+1} + \frac{2}{n^2 +2} + \ldots + \frac{n}{n^2 + n} < \frac{1}{2} + \frac{1}{2n}.
2
1
<
n
2
+
1
1
+
n
2
+
2
2
+
…
+
n
2
+
n
n
<
2
1
+
2
n
1
.
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