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1991 Chile National Olympiad
5
infinite sum a_j/2^j if a_n Fibonacci (Chile NMO 1991 P4)
infinite sum a_j/2^j if a_n Fibonacci (Chile NMO 1991 P4)
Source:
November 20, 2021
Fibonacci
number theory
algebra
Sum
Problem Statement
The sequence
(
a
k
)
(a_k)
(
a
k
)
,
k
>
0
k> 0
k
>
0
is Fibonacci, with
a
0
=
a
1
=
1
a_0 = a_1 = 1
a
0
=
a
1
=
1
. Calculate the value of
∑
j
=
0
∞
a
j
2
j
\sum_{j = 0}^{\infty} \frac{a_j}{2^j}
j
=
0
∑
∞
2
j
a
j
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