Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.1 ? 8 + 2 ? 8 + 3 ? 8 + . . . + 8n = 
What will be an ideal response?
First we show that the statement is true when n = 1.
For n = 1, we get 8 = 
= 8.
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.
1 ? 8 + 2 ? 8 + 3 ? 8 + . . . + 8k + 8(k + 1) = 
+ 8(k + 1)
= 
= 
Condition II is satisfied. As a result, the statement is true for all natural numbers n.
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Simplify the fraction.
A. 
B. 
C. 
D. 
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