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Miklós Schweitzer
1959 Miklós Schweitzer
5
Miklós Schweitzer 1959- Problem 5
Miklós Schweitzer 1959- Problem 5
Source:
October 30, 2015
college contests
Problem Statement
5. Denote by
c
n
c_n
c
n
the
n
n
n
th positive integer which can be represented in the form
c
n
=
k
l
(
k
,
l
=
2
,
3
,
…
)
c_n = k^{l} (k,l = 2,3, \dots )
c
n
=
k
l
(
k
,
l
=
2
,
3
,
…
)
. Prove that
∑
n
=
1
∞
1
c
n
−
1
=
1
\sum_{n=1}^{\infty}\frac{1}{c_n-1}=1
∑
n
=
1
∞
c
n
−
1
1
=
1
(N. 18)
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