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Official Ukraine Selection Cycle
Kyiv City MO
2021 Kyiv City MO
2021 Kyiv City MO Round 1
9.3
Slowly growing product
Slowly growing product
Source: Kyiv City MO 2021 Round 1, Problem 9.3
December 21, 2023
algebra
Problem Statement
Let
a
n
=
1
+
2
n
−
2
n
3
−
1
n
4
a_n = 1 + \frac{2}{n} - \frac{2}{n^3} - \frac{1}{n^4}
a
n
=
1
+
n
2
−
n
3
2
−
n
4
1
. For which smallest positive integer
n
n
n
does the value of
P
n
=
a
2
a
3
a
4
…
a
n
P_n = a_2a_3a_4 \ldots a_n
P
n
=
a
2
a
3
a
4
…
a
n
exceed
100
100
100
?
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