Answer to Question #160403 in Discrete Mathematics for Adil alvi

Question #160403

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


1
Expert's answer
2021-02-03T01:18:13-0500

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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