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Putnam
1961 Putnam
B7
B7
Part of
1961 Putnam
Problems
(1)
Putnam 1961 B7
Source: Putnam 1961
6/17/2022
Given a sequence
(
a
n
)
(a_n)
(
a
n
)
of non-negative real numbers such that
a
n
+
m
≤
a
n
a
m
a_{n+m}\leq a_{n} a_{m}
a
n
+
m
≤
a
n
a
m
for all pairs of positive integers
m
m
m
and
n
,
n,
n
,
prove that the sequence
(
a
n
n
)
(\sqrt[n]{a_n })
(
n
a
n
)
converges.
Putnam
Convergence
Sequences