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4. Prove each of the following statements using mathematical induction. (a) For every integer n > 1, 1 + 6 + 11 + 16 + ... + (5n - - 4) n(5n - 3) 2 (b) For every integer n > 3, 43 +44 +4% + . +4" = 4(4" 16) 3 (c) For every integer n > 1, 12 + n(n + 1)(2n +1) + '+ n 6 (d) For every integer n > 1, n i (i!) = (n + 1)! 1. i=1