Question

n!>= 2^(n-1), n>=1...proof by induction
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Answer 1

Answer:

Suppose that when n=k (k≥4), we have that k!>2k.

Now, we have to prove that (k+1)!>2k+1 when n=(k+1)(k≥4).

(k+1)!=(k+1)k!>(k+1)2k (since k!>2k)

That implies (k+1)!>2k⋅2 (since (k+1)>2 because of k is greater than or equal to 4)

Therefore, (k+1)!>2k+1

Finally, we may conclude that n!>2n for all integers n≥4