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Miklós Schweitzer
2011 Miklós Schweitzer
7
sequence
sequence
Source: miklos schweitzer 2011 q7
August 29, 2021
real analysis
Sequences
Problem Statement
prove that for any sequence of nonnegative numbers
(
a
n
)
(a_n)
(
a
n
)
,
lim inf
n
→
∞
(
n
2
(
4
a
n
(
1
−
a
n
−
1
)
−
1
)
)
≤
1
4
\liminf_{n\to\infty} (n^2(4a_n(1-a_{n-1})-1))\leq\frac{1}{4}
n
→
∞
lim
inf
(
n
2
(
4
a
n
(
1
−
a
n
−
1
)
−
1
))
≤
4
1
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