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I have a problem when trying to prove n! >= 2^(n-1).

My work:

Assuming n=k, k! >= 2^k-1 (induction hypothesis).

To prove true for n=k+1,

(k+1)! >= 2^(k+1)-1 = 2^k

Now considering R.S., 2^k = (2^(k-1))(2)

I get stuck here. I don't know how to continue onwards to prove that (k+1)! is >= 2^k.

Can anyone show what I did wrong or what I should've done?

My work:

Assuming n=k, k! >= 2^k-1 (induction hypothesis).

To prove true for n=k+1,

(k+1)! >= 2^(k+1)-1 = 2^k

Now considering R.S., 2^k = (2^(k-1))(2)

I get stuck here. I don't know how to continue onwards to prove that (k+1)! is >= 2^k.

Can anyone show what I did wrong or what I should've done?

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