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NCB Deposit # 45

Serigne Gningue
NCB Board Member

Understanding Infinite Series
An Introductory Paper Folding Illustration

Geometric Series

Serigne Gningue of Lehman College, City University of New York uses a paper folding activity to illustrate the same concept of a limit for a geometry series.

LEHMAN COLLEGE – The City University of New York
Department of Middle and High School Education

ESC 749: Methods of Teaching Mathematics in Grades 11-12
Professor Serigne Gningue   

Using A Model To Show The Sum Of A Series

a. Take one piece of paper and fold it in half.
b. Shade one half, leaving the other half blank. S1 represents the first shaded portion.
c. Fold again in fourths.
d. Shade one-fourth from the half that was left blank.
e. Write the total shaded portion as a fraction (S 2 ). Write the remaining non-shaded portion as a fraction under the second column. Fill out the third column.
f. Continue the process, filling out the columns up to S4 . If need be, find S5  and do the same.

g. Make a conjecture about Sn 
h. Prove Sn  using the Principle of Mathematical Induction (PMI).

Sum of Shaded Portion

as a Fraction

Non-Shaded Portion As a Fraction

Express Sum of Shaded Portion as a Difference

S1   =



S1   =

S2   =



S2   =

S3   =



S3   =

S4   =



S4   =

S5  =



S5   =







i. Prove your conjecture using the Principle of Mathematical Induction (PMI).

Derivation for a Geometric Series:

Complete derivation.



Useful Links and Ideas
Euler's work on series made him famous.