Principle Of Mathematical Induction Question 24

Question: The inequality $ n!>{2^{n-1}} $ is true for

Options:

A) $ n>2 $

B) $ n\in N $

C) $ n>3 $

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

  • [a] Let $ P(n)\equiv n!>{2^{n-1}};P(3)\equiv 6>4 $ Let $ P(k)\equiv k!>{2^{k-1}} $ is true.
    $ \therefore P(k+1)=(k+1)!=(k+1)k!>(k+1){2^{k-1}} $ $ >2^{k},(ask+1>2) $