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Miklós Schweitzer
1975 Miklós Schweitzer
8
Miklos Schweitzer 1975_8
Miklos Schweitzer 1975_8
Source: Sequences and Series
December 30, 2008
real analysis
real analysis unsolved
Problem Statement
Prove that if
∑
n
=
1
m
a
n
≤
N
a
m
(
m
=
1
,
2
,
.
.
.
)
\sum_{n=1}^m a_n \leq Na_m \;(m=1,2,...)
n
=
1
∑
m
a
n
≤
N
a
m
(
m
=
1
,
2
,
...
)
holds for a sequence
{
a
n
}
\{a_n \}
{
a
n
}
of nonnegative real numbers with some positive integer
N
N
N
, then
α
i
+
p
≥
p
α
i
\alpha_{i+p} \geq p \alpha_i
α
i
+
p
≥
p
α
i
for
i
,
p
=
1
,
2
,
.
.
.
,
i,p=1,2,...,
i
,
p
=
1
,
2
,
...
,
where
α
i
=
∑
n
=
(
i
−
1
)
N
+
1
i
N
a
n
(
i
=
1
,
2
,
.
.
.
)
.
\alpha_i= \sum_{n=(i-1)N+1}^{iN} a_n \;(i=1,2,...)\ .
α
i
=
n
=
(
i
−
1
)
N
+
1
∑
i
N
a
n
(
i
=
1
,
2
,
...
)
.
L. Leindler
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