10668
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Convergence of a Hyperpower Sequence
The limit of the hyperpower sequence
, or equivalently,
,
,
satisfies the equation
=
. The solutions are 2 and 4. In the graphic we show that the limit is 2.
Contributed by:
Soledad Mª Sáez Martínez
and
Félix Martínez de la Rosa
THINGS TO TRY
Gamepad Controls
SNAPSHOTS
DETAILS
F. Azarpanah, "Proof without Words: Convergence of the Hyperpower Sequence,"
Mathematics Magazine
,
77
(5), 2004 p. 393.
RELATED LINKS
Power Tower
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Convergence of a Hyperpower Sequence
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/ConvergenceOfAHyperpowerSequence/
Contributed by:
Soledad Mª Sáez Martínez
and
Félix Martínez de la Rosa
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
A Recursive Sequence Convergent to e
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
A Monotone Sequence Bounded by e
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Limit of the Sequence a^(1/n)
Izidor Hafner
Convergence of a Monotonic Sequence
Anik Debnath and Thomas Roxlo (The Harker School)
Uniform Convergence of a Sequence of Functions
A Convergent Sequence Satisfies the Cauchy Criterion
Izidor Hafner
Mapping a Convergent Sequence by a Continuous Function
Izidor Hafner
Limit of a Sequence
Izidor Hafner
Supremum of an Increasing Bounded Sequence
Izidor Hafner
Plot of a Geometric Sequence and Its Partial Sums
Aaron Dunigan AtLee
Related Topics
Calculus
Sequences
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+