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Putnam
1949 Putnam
B5
B5
Part of
1949 Putnam
Problems
(1)
Putnam 1949 B5
Source: Putnam 1949
3/20/2022
let
(
a
n
)
(a_{n})
(
a
n
)
be an arbitrary sequence of positive numbers. Show that
lim sup
n
→
∞
(
a
1
+
a
n
+
1
a
n
)
n
≥
e
.
\limsup_{n\to \infty} \left(\frac{a_1 +a_{n+1}}{a_{n}}\right)^{n} \geq e.
n
→
∞
lim
sup
(
a
n
a
1
+
a
n
+
1
)
n
≥
e
.
Putnam
Sequences