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Cauchy condensation test
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Mathematics
Area of mathematics
Analysis
Real analysis
Sequence and series
Series (mathematics)
Created
2026-10-03
Updated
2026-10-14
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If
(
a
n
)
is
a
nonnegative decreasing
sequence
, then
∑
n
≥
1
a
n
converges if and only if the condensed
series
∑
k
≥
0
2
k
a
2
k
converges. Comparing each dyadic block with its
first
and last terms proves both directions.
Ancestors
(7)
Series (mathematics)
Sequence and series
Real analysis
Analysis
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2017
/
ia
/
Paper 1
/
11F
/
a
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2017
/
ia
/
Paper 1
/
11F
/
b
/
Solution
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2013
/
Paper 1
/
19
/
d
/
Solution
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Cauchy condensation test
by
Wikipedia Bot
1
View more
The
Cauchy condensation test
is
a
convergence
test
used in the
analysis
of infinite
series
, particularly for
series
with non-negative terms. It provides
a
method to determine the convergence or
divergence
of
a
series
based on the behavior of
a
related
series
.
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