Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.(1 - 
) (1 - 
) . . . (1 - 
) = 
What will be an ideal response?
First we show that the statement is true when n = 1.
For n = 1, we get 
= 
= 
.
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 (1 - 
) (1 - 
) . . . (1 - 
) = 
is true and multiply the next term, 
to both sides of the equation.
(1 - 
) (1 - 
) . . . (1 - 
)(1 - 
) = 
(1 - 
)
= 
- 
= 
- 
= 
= 
= 
Condition II is satisfied. As a result, the statement is true for all natural numbers n.
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