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Putnam
1962 Putnam
B5
Putnam 1962 B5
Putnam 1962 B5
Source: Putnam 1962
May 21, 2022
Putnam
inequalities
Problem Statement
Prove that for every integer
n
n
n
greater than
1
:
1:
1
:
3
n
+
1
2
n
+
2
<
(
1
n
)
n
+
(
2
n
)
n
+
…
+
(
n
n
)
n
<
2.
\frac{3n+1}{2n+2} < \left( \frac{1}{n} \right)^{n} + \left( \frac{2}{n} \right)^{n}+ \ldots+\left( \frac{n}{n} \right)^{n} <2.
2
n
+
2
3
n
+
1
<
(
n
1
)
n
+
(
n
2
)
n
+
…
+
(
n
n
)
n
<
2.
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