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Monotonic and Bounded Sequences
•
A sequence is
increasing
if each term is larger than the previous one.
A
sequence is
decreasing
if each term is smaller than the previous one.
•
A sequence is
monotonic
if the terms are
nonincreasing
(
a
1
≥
a
2
≥
···
≥
a
n
≥
···) or
nondecreasing
(
a
1
≤
a
2
≤
···
≤
a
n
≤
··· ).
Increasing or decreasing sequences are
strictly monotonic
.
•
A sequence is
bounded from above
if there is a value that the terms never
exceed.
A sequence is
bounded from below
if there is a value below which the
terms never fall.
A
bounded
sequence is bounded from above and below.
•
If a sequence is monotonic and bounded, then it has a limit.
If each successive term of a sequence is larger than
the previous term, then the sequence is
increasing
.
If each successive term of a sequence is smaller
than the previous term, then the sequence is
decreasing
.
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 Spring '10
 hyon
 Mathematical analysis, Order theory, Monotonic function

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