Use mathematical induction to prove the following identities. (a) [5 points] For all integers n 1,...

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Use mathematical induction to prove the following identities. (a) [5 points] For all integers n 1, 1.2.3+2.3.4++n(n + 1)(n+ 2) = +n(n+1)(n+2) n(n+1)(n+2)(n+3) (b) [5 points] For all integers n > 1, n(n + 5) is a multiple of 6. (c) [5 points] For all integers n 0, 4 2 4 1+ + + 3 9 + (3) n n+1 2 = 31 3 (d) [5 points] Suppose that C1, C2, C3, ... is a sequence defined as follows: C = 3, C2-9 = Ck7Ck 110ck-2 for all integers k > 3 Prove that cn = 4.2"-5" for all integers n > 1. Activ Go to Use mathematical induction to prove the following identities. (a) [5 points] For all integers n 1, 1.2.3+2.3.4++n(n + 1)(n+ 2) = +n(n+1)(n+2) n(n+1)(n+2)(n+3) (b) [5 points] For all integers n > 1, n(n + 5) is a multiple of 6. (c) [5 points] For all integers n 0, 4 2 4 1+ + + 3 9 + (3) n n+1 2 = 31 3 (d) [5 points] Suppose that C1, C2, C3, ... is a sequence defined as follows: C = 3, C2-9 = Ck7Ck 110ck-2 for all integers k > 3 Prove that cn = 4.2"-5" for all integers n > 1. Activ Go to

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a Proof by Mathematical Induction Base Case For n 1 1 2 3 1 2 3 4 4 6 24 4 6 6 This holds true for n ... View the full answer