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Miklós Schweitzer
1957 Miklós Schweitzer
7
7
Part of
1957 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1957- Problem 7
Source:
10/18/2015
7. Prove that any real number x satysfying the inequalities
0
<
x
≤
1
0<x\leq 1
0
<
x
≤
1
can be represented in the form
x
=
∑
k
=
1
∞
1
n
k
x= \sum_{k=1}^{\infty}\frac{1}{n_k}
x
=
∑
k
=
1
∞
n
k
1
where
(
n
k
)
k
=
1
∞
(n_k)_{k=1}^{\infty}
(
n
k
)
k
=
1
∞
is a sequence of positive integers such that
n
k
+
1
n
k
\frac{n_{k+1}}{n_k}
n
k
n
k
+
1
assumes, for each
k
k
k
, one of the three values
2
,
3
2,3
2
,
3
or
4
4
4
. (N. 14)
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