10537
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Sum of Reciprocals of Triangular Numbers
The sum of the reciprocals of the triangular numbers is
.
For each
, the area of each colored rectangle in the graphic is
.
Contributed by:
Soledad Mª Sáez Martínez
and
Félix Martínez de la Rosa
THINGS TO TRY
Gamepad Controls
SNAPSHOTS
DETAILS
Reference: R. B. Nelsen, "Proof without Words: Sum of Reciprocals of Triangular Numbers,"
Mathematics Magazine
,
64
(3), 1991 p.167.
RELATED LINKS
Triangular Number
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Sum of Reciprocals of Triangular Numbers
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/SumOfReciprocalsOfTriangularNumbers/
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
Sum of the Alternating Harmonic Series (II)
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Sum of the Alternating Harmonic Series (I)
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Sum of a Geometric Series
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Sum of a Telescoping Series
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Sum of a Telescoping Series (II)
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Visual Computation of Three Geometric Sums
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Visualizing Euler's Constant
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
The Sum of the Harmonic Progression as an Integral
Tommy Zenth
Bounding Partial Sums of the Harmonic Series
Matt Clay
Plot of a Geometric Sequence and Its Partial Sums
Aaron Dunigan AtLee
Related Topics
Area
Calculus
Series
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+