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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).
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Sum of Shaded Portion
as a Fraction
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Non-Shaded Portion As a Fraction
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Express Sum of Shaded Portion as a Difference
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S1
=
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S1
=
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S2
=
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S2
=
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S3
=
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S3
=
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S4
=
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S4
=
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S5
=
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S5
=
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Conjecture: Sn
=
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i. Prove your conjecture using the Principle of Mathematical Induction
(PMI).
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