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.


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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.
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