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IMC
2015 IMC
3
3
Part of
2015 IMC
Problems
(1)
IMC2015, problem 3
Source: IMC2015
7/29/2015
Let
F
(
0
)
=
0
F(0)=0
F
(
0
)
=
0
,
F
(
1
)
=
3
2
F(1)=\frac32
F
(
1
)
=
2
3
, and
F
(
n
)
=
5
2
F
(
n
−
1
)
−
F
(
n
−
2
)
F(n)=\frac{5}{2}F(n-1)-F(n-2)
F
(
n
)
=
2
5
F
(
n
−
1
)
−
F
(
n
−
2
)
for
n
≥
2
n\ge2
n
≥
2
.Determine whether or not
∑
n
=
0
∞
1
F
(
2
n
)
\displaystyle{\sum_{n=0}^{\infty}\, \frac{1}{F(2^n)}}
n
=
0
∑
∞
F
(
2
n
)
1
is a rational number.(Proposed by Gerhard Woeginger, Eindhoven University of Technology)
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IMC2015