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Miklós Schweitzer
1960 Miklós Schweitzer
6
6
Part of
1960 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1960- Problem 6
Source:
11/21/2015
6. Let
{
n
k
}
k
=
1
∞
\{ n_k \}_{k=1}^{\infty}
{
n
k
}
k
=
1
∞
be a stricly increasing sequence of positive integers such that
lim
k
→
∞
n
k
1
2
k
=
∞
\lim_{k \to \infty} n_k^{\frac {1}{2^k}}= \infty
lim
k
→
∞
n
k
2
k
1
=
∞
Show that the sum of the series
∑
k
=
1
∞
1
n
k
\sum_{k=1}^{\infty} \frac {1}{n_k}
∑
k
=
1
∞
n
k
1
is an irrational number. (N. 19)
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