11481
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
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
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Three Sequences with Limit e
Izidor Hafner
Limit of the Sum of Two Sequences
Izidor Hafner
Limit of a Sequence
Izidor Hafner
Limit of the Sequence a^(1/n)
Izidor Hafner
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
Related Topics
Calculus
Sequences
High School Calculus and Analytic Geometry
High School Mathematics
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+