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2001 Moldova National Olympiad
Problem 7
limit of sum of a sequence
limit of sum of a sequence
Source: 2001 Moldova MO Grade 11 P7
April 13, 2021
Sequence
algebra
Problem Statement
Set
a
n
=
2
n
n
4
+
3
n
2
+
4
,
n
∈
N
a_n=\frac{2n}{n^4+3n^2+4},n\in\mathbb N
a
n
=
n
4
+
3
n
2
+
4
2
n
,
n
∈
N
. Prove that the sequence
S
n
=
a
1
+
a
2
+
…
+
a
n
S_n=a_1+a_2+\ldots+a_n
S
n
=
a
1
+
a
2
+
…
+
a
n
is upperbounded and lowerbounded and find its limit as
n
→
∞
n\to\infty
n
→
∞
.
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