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Limits of Sequences
This Demonstration shows the limit behavior for three different sequences: two convergent and one not. The vertical orange line, if present on the horizontal axis, represents the value
that corresponds to
in the definition of limit.
Contributed by:
Sandro Frigio
SNAPSHOTS
DETAILS
Snapshot 1: the behavior of a decreasing convergent sequence
Snapshot 2: the behavior of a general convergent sequence
Snapshot 3: the behavior of a nonconvergent sequence
Is it possible that there is a number
such that, no matter how small the value of
, there is a corresponding
so that, for all
, it follows that
?
For a nonconvergent sequence it is possible to see that this is not possible whichever is the value of the chosen limit.
The control
lets you choose the number of elements of the sequence to show in the plot.
RELATED LINKS
Limit
(
Wolfram
MathWorld
)
Sequence
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Limits of Sequences
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/LimitsOfSequences/
Contributed by:
Sandro Frigio
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