Which of the following shows the best next step to prove the following by mathem

Question

Which of the following shows the best next step to prove the following by mathematical induction? N! > 2^n, n >orequalto 4 When n = 1, the formula is valid because 4! > 2^4 24 > 16 Assuming that k! > 2^k Show that (k + 1)! > 2^k + 1 (k + 1)! = k! (k + 1) k!(k + 1) > k!(k + k) k!(k + 1) > 2^k(k + 1) k + 1 >orequalto 5 (k + k) > (k + 1)! Which of the following shows the best next step to prove the following by mathematical induction? 3^n > n middot 2^n, n >orequalto 1 When n = 1, the formula is valid because 3^1 > 1 middot 2^1 3 > 2 Assuming that 3^k > k middot 2^k You must show that 3^k + 1 > k + 1 middot 2^k + 1 You must show that 3^k + 1 > k middot 2^k + 1 You must show that 4^k > k middot 3^k You must show that 3^k + 1 > (k + 1)2^k + 1

Explanation / Answer

1A). Option B is the next step to proceed further.

1B). Option D is the next step to procedd futher.

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