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Sweden Contests
Swedish Mathematical Competition
1974 Swedish Mathematical Competition
1
b_n = \sum\limits_{r+s \leq n} a_ra_s if a_n = 2^{n-1}
b_n = \sum\limits_{r+s \leq n} a_ra_s if a_n = 2^{n-1}
Source: 1974 Swedish Mathematical Competition p1
March 26, 2021
Sequence
algebra
Sum
Problem Statement
Let
a
n
=
2
n
−
1
a_n = 2^{n-1}
a
n
=
2
n
−
1
for
n
>
0
n > 0
n
>
0
. Let
b
n
=
∑
r
+
s
≤
n
a
r
a
s
b_n = \sum\limits_{r+s \leq n} a_ra_s
b
n
=
r
+
s
≤
n
∑
a
r
a
s
Find
b
n
−
b
n
−
1
b_n-b_{n-1}
b
n
−
b
n
−
1
,
b
n
−
2
b
n
−
1
b_n-2b_{n-1}
b
n
−
2
b
n
−
1
and
b
n
b_n
b
n
.
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