(a) Prove that for n ≥ 2, 3 > 2n + n². (b) For any n ≥ 1, the factorial function, denoted by n!, is the product of all the positive integers through n: n! = 1. 2.3... (n-1) · n Prove that for n ≥ 4, n! > 2n. n Prove thatforn×1, Σ j=1 ≤2 1 n

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