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Canada National Olympiad
2021 Canada National Olympiad
2
Canadian MO 2021 P2
Canadian MO 2021 P2
Source:
March 12, 2021
algebra
inequalities
CMO
Canada
n-variable inequality
Problem Statement
Let
n
≥
2
n\geq 2
n
≥
2
be some fixed positive integer and suppose that
a
1
,
a
2
,
…
,
a
n
a_1, a_2,\dots,a_n
a
1
,
a
2
,
…
,
a
n
are positive real numbers satisfying
a
1
+
a
2
+
⋯
+
a
n
=
2
n
−
1
a_1+a_2+\cdots+a_n=2^n-1
a
1
+
a
2
+
⋯
+
a
n
=
2
n
−
1
.Find the minimum possible value of
a
1
1
+
a
2
1
+
a
1
+
a
3
1
+
a
1
+
a
2
+
⋯
+
a
n
1
+
a
1
+
a
2
+
⋯
+
a
n
−
1
\frac{a_1}{1}+\frac{a_2}{1+a_1}+\frac{a_3}{1+a_1+a_2}+\cdots+\frac{a_n}{1+a_1+a_2+\cdots+a_{n-1}}
1
a
1
+
1
+
a
1
a
2
+
1
+
a
1
+
a
2
a
3
+
⋯
+
1
+
a
1
+
a
2
+
⋯
+
a
n
−
1
a
n
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