Use mathematical induction to prove that the statement is true for every positive integer n.(1 - 
) (1 - 
) . . . (1 - 
) = 
What will be an ideal response?
Answers will vary. One possible proof follows.
a). Let n = 1. Then, (1 - 
) = 
= 
= 
. Thus, the statement is true for n = 1.
b). Assume the statement is true for n = k:
Sk = 
.
Also, if the statement is true for n = k + 1, then
Sk+1 = Sk ? (1 - 
) = 
Substitute to get:
? (1 - 
) = 
,
or
? (1 - 
) = 
.
Simplify:
? (
- 
) = 
? (
) = 
= 
Since the equality holds, then the statement is true for n = k + 1 as long as it is true for n = k. Furthermore, the statement is true for n = 1. Therefore, the statement is true for all natural numbers n.
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Solve the inequality and express the solution set in interval notation. Graph the solution set on the real number line.
? 
- 
A. x ? - 
; 
B. x ? -8; (-?, -8]
C. x ? 8; (-?, 8]
D. x ? -8; [-8, ?)
Use a calculator to find 
.
?
Please round the answer to the nearest ten-thousandth.
Fill in the blank(s) with the appropriate word(s).
Write the power of i as i, -1, -i, or 1.i14 + i11
A. 1 + i B. 1 - i C. -1 + i D. -1 - i
Simplify.
A. 12
B. 3
C. 3
D. 2