Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.12 + 42 + 72 + . . . + (3n - 2)2 = 
What will be an ideal response?
First we show that the statement is true when n = 1.
For n = 1, we get 1 = 
= 1.
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.
12 + 42 + 72 + . . . + (3k - 2)2 + (3(k + 1) - 2)2 = 
+ (3(k + 1) - 2)2
= 
+ (3k + 1)2
= 
+ 
= 
= 
Simplify the expression 
to verify:
= 
= 
= 
= 
Condition II is satisfied. As a result, the statement is true for all natural numbers n.
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Find all cube roots of the complex number. Leave answers in trigonometric form.125
A. 5 cis 90°, 5 cis 210°, 5 cis 330° B. 5 cis 0°, 5 cis 60°, 5 cis 120° C. 5 cis 45°, 5 cis 165°, 5 cis 325° D. 5 cis 0°, 5 cis 120°, 5 cis 240°
Perform the indicated operations and express your answer in the form a + bi. 
A. 10i B. 10 C. -10i D. -10
Approximate the area under the curve and above the x-axis using n rectangles. Use left endpoints.f(x) = 
from x = -2 to x = 9; n = 4
A. 
B. 
C. 
D. 
Add or subtract as indicated. Write the answer in lowest terms.
+ 
A. 
B. 
C. 
D. 