Limits of Sequences

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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 (March 2011)
Open content licensed under CC BY-NC-SA



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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