Use mathematical induction to prove the statement is true for all positive integers n.7n > n
What will be an ideal response?
Answers may vary. Possible answer:
First, we show the statement is true when n = 1.
For n = 1, 71 > 1
So P1 is true and the first condition for the principle of induction is satisfied.
Next, we assume the statement holds for some unspecified natural number k. That is,
Pk: 7k > k is assumed true.
On the basis of the assumption that Pk is true, we need to show that Pk+1 is true.
Pk+1: 7k+1 > k + 1
So we assume that 
is true and multiply both sides of the equation by 7
7k? 7 > k7
7k+1 > k + 6k
7k+1 > k + 1 since 6k > 1
So Pk+1 is true if Pk is assumed true. Therefore, by the principle of mathematical induction, 
for all natural numbers n.
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A. 
B. 
C. 
D. (mn)-7
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A. 2 hr, 32.15 min B. 2 hr, 16.08 min C. 2 hr, 16.53 min D. 2 hr, 33.07 min
Find the area of the figure.
A. 39
B. 286
C. 13 
D. 13 
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