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10
2017 Guts #10: Weird limit
2017 Guts #10: Weird limit
Source:
February 21, 2017
geometry
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle in the plane with
A
B
=
13
AB = 13
A
B
=
13
,
B
C
=
14
BC = 14
BC
=
14
,
A
C
=
15
AC = 15
A
C
=
15
. Let
M
n
M_n
M
n
denote the smallest possible value of
(
A
P
n
+
B
P
n
+
C
P
n
)
1
n
(AP^n + BP^n + CP^n)^{\frac{1}{n}}
(
A
P
n
+
B
P
n
+
C
P
n
)
n
1
over all points
P
P
P
in the plane. Find
lim
n
→
∞
M
n
\lim_{n \to \infty} M_n
lim
n
→
∞
M
n
.
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