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1
Albanian TST 2014 1st problem
Albanian TST 2014 1st problem
Source:
April 21, 2014
inequalities
induction
algebra proposed
algebra
Problem Statement
Prove that for
n
≥
2
n\ge 2
n
≥
2
the following inequality holds:
1
n
+
1
(
1
+
1
3
+
…
+
1
2
n
−
1
)
>
1
n
(
1
2
+
…
+
1
2
n
)
.
\frac{1}{n+1}\left(1+\frac{1}{3}+\ldots +\frac{1}{2n-1}\right) >\frac{1}{n}\left(\frac{1}{2}+\ldots+\frac{1}{2n}\right).
n
+
1
1
(
1
+
3
1
+
…
+
2
n
−
1
1
)
>
n
1
(
2
1
+
…
+
2
n
1
)
.
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