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.

Mathematics

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