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2012 Centers of Excellency of Suceava
2
A not so hard limit
A not so hard limit
Source:
October 31, 2019
function
limits
Problem Statement
Calculate
lim
n
→
∞
f
(
1
)
+
(
f
(
2
)
)
2
+
⋯
+
(
f
(
n
)
)
n
(
f
(
n
)
)
n
,
\lim_{n\to\infty } \frac{f(1)+(f(2))^2+\cdots +(f(n))^n}{(f(n))^n} ,
lim
n
→
∞
(
f
(
n
)
)
n
f
(
1
)
+
(
f
(
2
)
)
2
+
⋯
+
(
f
(
n
)
)
n
,
where
f
:
R
⟶
R
>
0
f:\mathbb{R}\longrightarrow\mathbb{R}_{>0 }
f
:
R
⟶
R
>
0
is an unbounded and nondecreasing function. Dan Popescu
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