Answer to Question #186615 in Discrete Mathematics for Maricel

Question

MATHEMATICAL INDUCTION AND RECURRENCE

1. What is the base case for inequality 3n > n2 , where n = 2? (2 pts)

A. 3 > 1

B. 9 > 4

C. 6 > 4

D. 4 < 9

2.For the mathematical induction to be true, what type of number should be the value of n?

A. natural number B. imaginary number C. rational number D. whole number

3. What would be the hypothesis of the mathematical induction for x(x + 1) < x! , where x ≥ 7?

A. It is assumed that at x = k, k(k + 1)! < k!

B. It is assumed that at x = k, k(k + 1)! > k!

C. It is assumed that at x = k, k(k + 1)! < (k + 1)!

D. It is assumed that at x = k, k(k + 1)(k + 2)! < k!

4. For any positive integer x, ________ is divisible by 5 (2 pts)

A. 5x2 + 5 B. 2x + 4 C. x4 + 5x D. 3x2 + 2

Answer 1

1.

C. 6 > 4

2.

A. natural number

3.

for x(x + 1) < x! :

It is assumed that at x = k,

$(k+1)(k+2)<(k+1)!$

$k+2<k!$

Answer: B. It is assumed that at x = k, k(k + 1)! > k!

4.

A. $5\cdot2+5$