Math Topics

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Sums of Integers and Series

Source of topics for this section

"Proofs Without Words" (ref 4,5) by R.B.Nelson,and "The Book of Numbers" (Ref 2) by Conway and Guy contains many beautiful drawings, which inspired me to express simple summations in more dynamic ways using CAD software.
For Bernoulli number, Ref.3 ,7 are used for explaining details.
Ref, 1,6 & 8 are good for general readings .

Sums of Integer , integer squared, cubed and raised to higher power

  1. Sum of N equally spaced numbers

  2. Sum of square from 1 to N2

  3. Sum of cube from 1 to N3

  4. Sum of 1 to Nm, (m P 4)

Geometric Series

  1. Infinite series sum of ratio= 1/4


  1. Wells, David: The Penguin Dictionary of Curious and Interesting GEOMETRY. London,England: Penguin Books, p.198, 1991.(Out of print)

  2. Conway,J.H., Guy,R.K.: The Book of Numbers. Springer-Verlag,New York, pp.27-62, 1995.

  3. Young,Robert M.: Excursions in Calculus. Mathematical Association of America. 1992.

  4. Nelson,R.B. : Proofs Without Words: Exercises in Visual Thinking. MAA, p.69,71,72,77,87,122 1993.

  5. Nelson,R.B. : Proofs Without Words II: More Exercises in Visual Thinking. MAA,p.111 ,2000.

  6. Heath, Sir L.H.: A manual of Greek Mathematics. Dover Edition ,1963. pp. 36-50 ,Originally published in 1931.

  7. Smith, David Eugene: A Source Book in Mathematics. Dover, 1959. Originally pulished in 1929.

  8. Wells, David: The Penguin Dictionary of Curious and Interesting NUMBERS. London,England: Penguin Books, p.85, 1986.

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Last Updated July 9-th, 2006

Copyright 2006 Takaya Iwamoto   All rights reserved.