MAT 243 Online Written Homework
Assignments for Week 10/15
Before you start these assignments, you must have studied and understood the common
mistakes on inductive proof writing given in the lecture. Specifically,
โข
do not use the notation P(n) to refer to both the statement to be proved and to a
quantity that P(n) is making a statement about. It is best if you do not use the
notation P(n) at all.
โข
do not confuse stating P(n+1) with proving it.
โข
in proofs of summation formulas, do not assume that the (n+1)th term of the
summation is n+1.
โข
do not employ the โrenaming ritualโ.
โข
in proofs of summation formulas, do not confuse the running variable in the sigma
sum with the variable that represents the upper limit of the summation.
โข
make sure to write the correct inductive hypothesis.
1.
Prove using induction for all positive integers
?
that
โ ๐(๐ + 1)
๐
๐=1
=
1
3
?(? + 1)(? + 2).
:
1
1
:
.

ยฉ2018 R. Boerner ASU School of Mathematical and Statistical Sciences

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