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By using mathematical induction prove that (n+1)! > 2^(n+1) for n, where n is a positive integer greater than or equal to 4

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The result is trivially true for k=4 since, (4+1)!=120>32=2^{5}. Lets us assume it to be true for k=n. We prove for k=n+1. Now,

(n+2)!=(n+1)!(n+2)>2^{n+1}(n+2) by induction hypothesis. Now n>4\Rightarrow n+2>6 >2. Hence we get, 2^{n+1}(n+ 2)>2^{n+1}\times 2=2^{n+2}. So we are done by induction.


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