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Mathematical induction proof?

what is the most simplest method to solve this question by using mathematical induction to prove that $$n !>2^n-1$$ and integers $$n>5$$?

Note by Syed Hissaan
1 year, 2 months ago

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@Calvin Lin @Chung Kevin , any proof for that one !

- 1 year, 2 months ago

What have you tried? What have you done?

Seems to me like a simple induction proof starting with base case of $$n = 6$$.

Staff - 1 year, 2 months ago

is it valid in this type of proof to place any value of the k < 6 on one of the side to setup our equations)# for n=k e.g : $$(k+1)!> 2^k .2 -1 +2^k -k$$ can we take k<4 * or *k=2on the R.H.S to proof our question

- 1 year, 2 months ago

No, because the statement is not true for $$k \leq 4$$. That is why you have to start the base case in the appropriate domain of $$n > 5$$ (or whatever they tell you to).

Staff - 1 year, 2 months ago

ok thanks !

- 1 year, 2 months ago