Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.9 + 18 + 27 + ... + 9n = 
What will be an ideal response?
First, we show the statement is true when n = 1.
For n = 1, we get 9 = 
= 9.
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.
Condition II is satisfied. As a result, the statement is true for all natural numbers n.
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Solve the problem.The profile formed by y = 
for 
is rotated about the 
to form a dome. Find the volume of the dome if the units are meters.
A. 11,970,222 m3 B. 271 m3 C. 13,029 m3 D. 4147 m3
For the given function f(x), find a bound for the indicated remainder term on the given interval.f(x) = (1 + x)-3; R2; a = 0; [-0.5, 0.5]
A. 48.0000 B. 80.0000 C. 0.1097 D. 1.3333
Give an appropriate answer.Let
f(x) = -10 and
g(x) = 8. Find
[f(x) ? g(x)].
A. 2 B. -80 C. -2 D. 8
Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.-2(x + 7) + (-5x) = -7(x - 7) + 5
A. Contradiction; ? B. Identity; {all real numbers} C. Conditional; {0} D. Conditional; {5}