Back to . . . 

Curve Bank Home

Deposit #44

A Streaming Video

NCB logo
Understanding Infinite Series in the Calculus

  with Professor Robert Meyer, CSULA
Picture Dr. Robert Meyer 

Geometric Series

Geometric series equation 
 
Two Options for viewing:

FITSC Lab and Video




1.    Quiz #1   .


2.
    Quiz #2   .

3.    Quiz #3   .


4
.   Quiz #4   .

5.    Quiz #5   .

6.    Quiz #6   .


7.
    Quiz #7  

8.    Quiz # 8   .

9.    Quiz #9   .


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,  Augustin-Louis 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. 137-141.


Derivation for a Geometric Series:
1.
Steps in derivation
4.
Complete derivation.
Derivation completed
2.
Steps in derivation
3.
Steps in derivation

Useful Links and Books
http://www.research.att.com/~njas/sequences           from   Logo of link
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. 43-47.
Carl B. Boyer revised by Uta C. Merzbach, A History of Mathematics, 2nd ed,. John Wiley and Sons, 1989, pp.  514-517.
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. 137-141.

Victor J. Katz, A Brief History of Mathematics, BRIEF VERSION, Pearson Addison Wesley, 2004, pp. 434-437.
Eric W. Weisstein, "Series" in CRC Concise Encyclopedia of MATHEMATICS, CRC Press, 1998,  p. 1618.
Harmonic Series
     James Lesko, Sums of Harmonic-Type Series, The College Mathematics Journal, Vol.35, No.3, May 2004, pp. 171-182.
     Curtis Feist and Ramin Naimi, Almost Alternating Harmonic Series, The College Mathematics Journal, Vol.35, No.3, May 2004, pp. 183-191.
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
Home link
FITSC Lab contributions by
Humna Khan
Nick Mew
Matthew Nelson
Hong Kha