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7
Math Prize 2017 Problem 7
Math Prize 2017 Problem 7
Source:
September 26, 2017
Math Prize for Girls
Problem Statement
Let
a
1
a_1
a
1
,
a
2
a_2
a
2
, ... be an infinite sequence of integers such that
0
≤
a
k
≤
k
0 \le a_k \le k
0
≤
a
k
≤
k
for every positive integer
k
k
k
and such that
2017
=
∑
k
=
1
∞
a
k
⋅
k
!
.
2017 = \sum_{k = 1}^\infty a_k \cdot k! \, .
2017
=
k
=
1
∑
∞
a
k
⋅
k
!
.
What is the value of the infinite series
∑
k
=
1
∞
a
k
\sum_{k = 1}^\infty a_k
∑
k
=
1
∞
a
k
?
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