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Vietnam Contests
Vietnam National Olympiad
1983 Vietnam National Olympiad
2
Finding the larger of two algebraic expressions
Finding the larger of two algebraic expressions
Source: Vietnam MO 1983 P5
March 18, 2011
inequalities proposed
inequalities
Problem Statement
Decide whether
S
n
S_n
S
n
or
T
n
T_n
T
n
is larger, where
S
n
=
∑
k
=
1
n
k
(
2
n
−
2
k
+
1
)
(
2
n
−
k
+
1
)
,
T
n
=
∑
k
=
1
n
1
k
S_n =\displaystyle\sum_{k=1}^n \frac{k}{(2n - 2k + 1)(2n - k + 1)}, T_n =\displaystyle\sum_{k=1}^n\frac{1}{k}
S
n
=
k
=
1
∑
n
(
2
n
−
2
k
+
1
)
(
2
n
−
k
+
1
)
k
,
T
n
=
k
=
1
∑
n
k
1
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