LEHMAN COLLEGE – The City University of New York
Department of Middle and High School Education
ESC 749: Methods of Teaching Mathematics in Grades 1112
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. S_{1} represents the first shaded
portion.
c. Fold again in fourths.
d. Shade onefourth from the half that was left blank.
e. Write the total shaded portion as a fraction (S _{2} ).
Write the remaining nonshaded portion as a fraction under the second
column. Fill out the third column.
f. Continue the process, filling out the columns up to S_{4} .
If need be, find S_{5} and do the same.
g. Make a conjecture about S_{n}
h. Prove S_{n} using the Principle
of Mathematical Induction (PMI).
Sum of Shaded Portion
as a Fraction

NonShaded Portion As a Fraction

Express Sum of Shaded Portion as a Difference

S_{1
}=


S_{1
}=

S_{2 }_{ }_{ }
=


S_{2 }_{ }_{ }
=

S_{3
}
=


S_{3
}
=

S_{4
}
=


S_{4
}
=

S_{5 }
=


S_{5
}
=

Conjecture: S_{n
}
=



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