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South Korea USCM
2017 Korea USCM
3
3
Part of
2017 Korea USCM
Problems
(1)
Find limit, recurrence relation
Source: 2017 South Korea USCM P3
8/15/2020
Sequence
{
a
n
}
\{a_n\}
{
a
n
}
defined by recurrence relation
a
n
+
1
=
1
+
n
2
a
n
a_{n+1} = 1+\frac{n^2}{a_n}
a
n
+
1
=
1
+
a
n
n
2
. Given
a
1
>
1
a_1>1
a
1
>
1
, find the value of
lim
n
→
∞
a
n
n
\lim\limits_{n\to\infty} \frac{a_n}{n}
n
→
∞
lim
n
a
n
with proof.
real analysis
limit
recurrence relation
college contests