Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
is divisible by 2
What will be an ideal response?
First, we show that the statement is true when n = 1.
For 
This is a true statement and Condition I is satisfied.
Next, we assume the statement holds for some k. That is,
is divisible by 2 is true for some positive integer k.
We need to show that the statement holds for 
. That is, we need to show that
is divisible by 2.
So we assume 
is divisible by 2 and look at the expression for n = k + 1.
Since 
is divisible by 2, then 
for some integer m. Hence,
Condition II is satisfied. As a result, the statement is true for all natural numbers n.
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A. 
; 91.8 beats per minute
B. 
; 95.5 beats per minute
C. 
; 0.011 beats per minute
D. 
; 85.4 beats per minute
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A. (0, 0)
B. (0, 0)
C. (0, 4)
D. (0, 0)
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per year compounded daily to triple in value. Find the answer to the nearest year.
A. 0 years B. 23 years C. 3,049,422 years D. 30,692 years
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A. ln 81 B. ln 3 C. ln 27 D. ln 27 - 6