# prove by induction that 2^n/n! < 4/n [closed]

How do I do this?

I know how to do the base case but I can't figure out how to do the next steps.

## closed as off-topic by Xander Henderson, John Omielan, max_zorn, Dbchatto67, LeucippusApr 19 at 5:48

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Xander Henderson, John Omielan, max_zorn, Dbchatto67, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.

## 1 Answer

Hint: We can write $$2^{n-2}\cdot n<4\cdot n!$$ by cross multiplication and this is $$2^{n-2}<(n-1)!$$, which is easier to prove. and we have to prove that $$2^{n-1} if $$2^{n-2}<(n-1)!$$ multiplying this inequality by $$2$$ we get $$2^{n-1}<2(n-1)!$$ and $$2(n-1)! for $$n>2$$