Notice that if we expand out 38 < 8! we get 6561 < 40320 which is clearly true! The above induction proof showed that 3" < n! for n > the following which are correct about the above proof. a. Actually if we expand out 38 < 8! we don't get 6561 < 40320, and in fact n = 8 does not work either! b. The proof is incomplete because the base case should start at n = 1. O C. The theorem 3" < n! for n > 9 is incorrect, and we are being asked to consider a correct proof of an incorrect theorem! O d. Since we have missed the case n = 8 the proof itself is incorrect. e. The proof is correct, but we could prove more. Of. The proof shows that 3" < n! for n 2 9, hence for n < 9 we have 3" > n!. g. There is a mistake in the base case.
Notice that if we expand out 38 < 8! we get 6561 < 40320 which is clearly true! The above induction proof showed that 3" < n! for n > the following which are correct about the above proof. a. Actually if we expand out 38 < 8! we don't get 6561 < 40320, and in fact n = 8 does not work either! b. The proof is incomplete because the base case should start at n = 1. O C. The theorem 3" < n! for n > 9 is incorrect, and we are being asked to consider a correct proof of an incorrect theorem! O d. Since we have missed the case n = 8 the proof itself is incorrect. e. The proof is correct, but we could prove more. Of. The proof shows that 3" < n! for n 2 9, hence for n < 9 we have 3" > n!. g. There is a mistake in the base case.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Notice that if we expand out 3° < 8! we get 6561 < 40320 which is clearly true! The above induction proof showed that 3" < n! for n > 9. With this in mind mark all|
the following which are correct about the above proof.
a. Actually if we expand out 3° < 8! we don't get 6561 < 40320, and in fact n =
8 does not work either!
b. The proof is incomplete because the base case should start at n =
= 1.
c. The theorem 3" < n! for n > 9 is incorrect, and we are being asked to consider a correct proof of an incorrect theorem!
d. Since we have missed the casen =
8 the proof itself is incorrect.
e. The proof is correct, but we could prove more.
f.
The proof shows that 3" < n! for n > 9, hence for n < 9 we have 3" > n!.
g. There is a mistake in the base case.
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