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58
a_n <= a_{n+m} <= a_n + a_m
a_n <= a_{n+m} <= a_n + a_m
Source:
October 11, 2010
inequalities
limit
algebra unsolved
algebra
Problem Statement
Let
(
a
n
)
1
∞
(a_n)_1^{\infty}
(
a
n
)
1
∞
be a sequence such that
a
n
≤
a
n
+
m
≤
a
n
+
a
m
a_n \le a_{n+m} \le a_n + a_m
a
n
≤
a
n
+
m
≤
a
n
+
a
m
for all positive integers
n
n
n
and
m
m
m
. Prove that
a
n
n
\frac{a_n}{n}
n
a
n
has a limit as
n
n
n
approaches infinity.
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