Use mathematical induction to establish each of the following inequalities.
(a) [BB] 2n > n2,for n ≥ 5.
(b)
(c) [BB] n! > n3 for all n ≥ 6.
(d) , for n ∈ N.
(e) For any x ∈ R, x > − 1, (1 + x)n ≥ 1 + nx for all n ∈ N.
(f) For any integer n > 2,
(g) for all n ≥ 2
(h) for n ≥ 2.
(i) [BB] 1 (3)(5) … (2n − 1) ≥ 2(4)(6) … (2n − 2) for every integer n ≥ 2.
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