About Site Map Submit Contact Us Log in | Create an account
Create an account Log In
Average Rating
User Rating:
Visitors Rating:
My rating:

Write review
  • Last update: 5 years ago
  • Total downloads: 111
  • Operating system: Linux, Mac OS X, Win All, BSD, Solaris
  • Publisher: Thomas Schmelzer
See full specifications

scripts default iconSumming Kempner's Curious (Slowly-Convergent) Series (Scripts) Publisher's description

This package shows how to compute the sum of some very strange convergent series.

This package shows how to compute the sum of some very strange convergent series.

The harmonic series 1/1 + 1/2 + 1/3 + ... + 1/n + ... diverges. This means that the sum can be made as large as desired by adding enough terms.

Suppose we delete from this series all terms with a "9" in the denominator. That is, we remove 1/9, 1/19, 1/29, etc. Then the remaining series converges to a sum less than 80. This very surprising result was proved by A. J. Kempner in 1914.

We also get convergent series if we pick any other digit string (say, "314159") and compute the sum of 1/n where n contains no "314159".

Unfortunately, these series converge so slowly that it is impossible to compute their sums simply by adding up terms. A more sophisticated algorithm is required. As a result, this computational problem has attracted much interest over the years.

The article, "Summing a Curious, Slowly Convergent Series" by Thomas Schmelzer and Robert Baillie in the American Mathematical Monthly, vol. 115, pages 525-540 (June/July 2008) has an algorithm that computes sums of these and related series quickly, and to high precision.

This MATLAB implementation computes the sum of the "no 42" series. This problem is stated in the Appendix of the book "The SIAM 100 Digit challenge".

see also: http://library.wolfram.com/infocenter/MathSource/7166/

System Requirements:

MATLAB 7.6 (R2008a)
Program Release Status: New Release
Program Install Support: Install and Uninstall

Summing Kempner's Curious (Slowly-Convergent) Series (Scripts) Tags:

Click on a tag to find related softwares

Is Summing Kempner's Curious (Slowly-Convergent) Series (Scripts) your software?

Manage your software

Most Popular

scripts default icon ASK, OOK, FSK, BPSK, QPSK, 8PSK modulation 1.1
ASK, OOK, FSK, BPSK, QPSK, 8PSK modulation contain several functions for digital modulation simulation
scripts default icon Simulink Communication Labs 1.1
Simulink Communication Labs allows you to learn communication systems in greater depth.
scripts default icon M-QAM modulation and demodulation 1.1
M-QAM modulation and demodulation is the QAM modulation and demodulation tech.
scripts default icon LZW Compression/Decompression 1.1
LZW Compression/Decompression - Updated LZW compressor and decompressor with reasonable performance
scripts default icon InSPIRE utility to plot a 2D displacement field (Scripts) 1.0
This program plots the deformation field (displace vectors) contained in vector.txt.