Back to . . .  Curve Bank Home Dr. Meyer's Streaming Video 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   = Conjecture: Sn   =

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

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