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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Find the exact area of the surface obtained by rotating the given curve about the x-axis.
 FIGURE 1.png)
If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.8y2 + 36y - 20
A. 8x2 - 36x - 20 B. (8y - 4)(y + 5) C. 4(2y + 1)(y - 5) D. 4(2y - 1)(y + 5)
Determine whether the polynomial function is cubic or quartic.
A. Cubic B. Quartic
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. x + y + z = 92x - 3y + 4z = 7
A. {(- 
z + 
, 
z + 
, z)}
B. {(
, 
, 1)}
C. ?
D. {(
z + 
, - 
z + 
, z)}