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Putnam
1963 Putnam
A4
A4
Part of
1963 Putnam
Problems
(1)
Putnam 1963 A4
Source: Putnam 1963
5/1/2022
Let
(
a
n
)
(a_n)
(
a
n
)
be a sequence of positive real numbers. Show that
lim sup
n
→
∞
n
(
1
+
a
n
+
1
a
n
−
1
)
≥
1
\limsup_{n \to \infty} n \left(\frac{1 +a_{n+1}}{a_n } -1 \right) \geq 1
n
→
∞
lim
sup
n
(
a
n
1
+
a
n
+
1
−
1
)
≥
1
and prove that
1
1
1
cannot be replaced by any larger number.
Putnam
Limsup
Sequence