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Chile National Olympiad
2012 Chile National Olympiad
2
sum 1/a_i <=80
sum 1/a_i <=80
Source: Chile Finals 2012 L2 p2
October 5, 2022
number theory
Sum
inequalities
Problem Statement
Let
a
1
,
a
2
,
.
.
.
,
a
n
a_1,a_2,...,a_n
a
1
,
a
2
,
...
,
a
n
be all positive integers with
2012
2012
2012
digits or less, none of which is a
9
9
9
. Prove that
1
a
1
+
1
a
2
+
.
.
.
+
1
a
n
≤
80.
\frac{1}{a_1}+\frac{1}{a_2}+ ... +\frac{1}{a_{n}}\le 80.
a
1
1
+
a
2
1
+
...
+
a
n
1
≤
80.
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