Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.3 + 3 ?
+ 3 ?
2 + ... + 3 ?
n - 1 = 
What will be an ideal response?
First we show that the statement is true when n = 1.
For n = 1, we get 3 = = 3.
This is a true statement and Condition I is satisfied.
Next, we assume the statement holds for some k. That is,
is true for some positive integer k.
We need to show that the statement holds for k + 1. That is, we need to show that
So we assume that is true and add the next term,
to both sides of the equation.
3 + 3 ? + 3 ?
2 + ... + 3 ?
k - 1 + 3 ?
(k + 1) - 1=
+ 3 ?
(k + 1) - 1
= + 3
k
= +
=
=
=
Condition II is satisfied. As a result, the statement is true for all natural numbers n.
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A.
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