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5
2015 Algebra #5
2015 Algebra #5
Source:
July 1, 2022
2015
Algebra Test
Problem Statement
The Fibonacci numbers are a sequence of numbers defined recursively as follows:
F
1
=
1
F_1=1
F
1
=
1
,
F
2
=
1
F_2=1
F
2
=
1
, and
F
n
=
F
n
−
1
+
F
n
−
2
F_n=F_{n-1}+F_{n-2}
F
n
=
F
n
−
1
+
F
n
−
2
. Using this definition, compute the sum
∑
k
=
1
10
F
k
F
k
+
1
F
k
+
2
.
\sum_{k=1}^{10}\frac{F_k}{F_{k+1}F_{k+2}}.
k
=
1
∑
10
F
k
+
1
F
k
+
2
F
k
.
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