Back to . . .
Curve Bank Home
Deposit #44
A Streaming Video

Understanding
Infinite Series in the Calculus
with Professor Robert Meyer, CSULA


Be patient.
Be sure to wait until
you hear
Dr. Meyer's voice.
Geometric
Series


Convergence
occurs only if the various sums "taken, from the first, in whatever
number one wishes, finish by constantly have an absolute value less
than any assignable limit."
Cours
d'analyse de l'Ecole Royale Polytechnique, VI, AugustinLouis
Cauchy
[An
invaluable insight offered without proof from Cauchy's lecture notes.]
~~~~~
"The
way mathematicians think is not just a matter of individual
inclination. Rather, it is a product of education and culture."
,Judith V. Grabiner, The Calculus as Algebra, the Calculus as
Geometry: Lagrange, Maclaurin, and their Legacy,
published in Ronald Calinger, ed., VITA MATHEMATICA, The
MAA, 1996, pp. 137141.

Derivation for a Geometric Series:
1.

4.
Complete
derivation.

2.

3.


Useful
Links and Books

http://www.research.att.com/~njas/sequences
from

Another
version of converging geometric series using paper folding is a deposit
in the NCB by Serigne Gningue. 
Beata Randriananoanina, A Visual
Approach to Geometric Series, The College Mathematics Journal,
Vol.35, No.1, January, 2004, pp. 4347.

Carl B. Boyer revised by Uta C.
Merzbach, A History of Mathematics, 2nd ed,. John Wiley and
Sons, 1989, pp. 514517.

Howard Eves, An Introduction to
the History of Mathematics, 6th ed,. The Saunders College
Publishing, 1990, p. 488.

Grabiner, Judith V., The Calculus as
Algebra, the Calculus as Geometry: Lagrange, Maclaurin, and their
Legacy, published in
Calinger, Ronald, ed., VITA MATHEMATICA, The MAA, 1996, pp.
137141.

Victor J. Katz, A Brief History
of Mathematics, BRIEF VERSION, Pearson Addison
Wesley, 2004, pp. 434437.

Eric W. Weisstein,
"Series" in CRC Concise Encyclopedia of MATHEMATICS,
CRC Press, 1998, p. 1618.

Harmonic Series
James Lesko, Sums of HarmonicType Series,
The College Mathematics Journal, Vol.35,
No.3, May 2004, pp. 171182.
Curtis Feist and Ramin Naimi, Almost
Alternating Harmonic Series, The College Mathematics
Journal, Vol.35, No.3, May 2004, pp. 183191.

Full Proofs
K. Knopp, Theory and
Application of Infinite Series, Hafner, 1951.

Information Technology Services
Taping and streaming
by
William
Stellmacher
Dennis Kimura
Wing T. (Sterling)
Wong


FITSC
Lab contributions by
Humna
Khan
Nick Mew
Matthew Nelson
Hong Kha


