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Moldova Team Selection Test
1998 Moldova Team Selection Test
12
Compute $\sum_{n=0}^{3^k} \frac{1}{b_n}$
Compute $\sum_{n=0}^{3^k} \frac{1}{b_n}$
Source: Moldova TST 1998
August 8, 2023
Problem Statement
Let
k
k{}
k
be a positive integer. For every positive integer
n
≤
3
k
n \leq 3^k
n
≤
3
k
, denote
b
n
b_n
b
n
the greatest power of
3
3
3
that divides
C
3
k
n
C_{3^k}^n
C
3
k
n
. Compute
∑
n
=
1
3
k
−
1
1
b
n
\sum_{n=1}^{3^k-1} \frac{1}{b_n}
∑
n
=
1
3
k
−
1
b
n
1
.
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