Binomial Theorem And Its Simple Applications Question 59
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},(k+1>2) $
BETA
