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
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.
Permanent Citation
Three Sequences with Limit e
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Limit of the Sum of Two Sequences
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Limit of a Sequence
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Limit of the Sequence a^(1/n)
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Convergence of a Hyperpower Sequence
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Convergence of a Monotonic Sequence
Anik Debnath and Thomas Roxlo (The Harker School)
Uniform Convergence of a Sequence of Functions
A Monotone Sequence Bounded by e
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
A Recursive Sequence Convergent to e
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
A Convergent Sequence Satisfies the Cauchy Criterion
Izidor Hafner
