1. Use induction to prove that 1 3+2+3+ +n = n (n + 1) /4 for...

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1. Use induction to prove that 1 3+2³+3³+ +n³ = n² (n + 1)² /4 for all integers n ≥ 1. 2. Use induction to prove that the following identity holds for all integers n ≥ 1:1+3+5++ (2n-1) = n 2. Exercises 3.5 1. Use induction to prove that n(n + 1)(n + 2) is a multiple of 3 for all integers n ≥ 1. 2. Use induction to show that n³ + 5n s a multiple of 6 for any nonnegative integer n. Exercises 3.6 1. Use mathematical induction to prove the identity F 21+F22+F23+ · · · + for any integer n ≥ 1. ++ F2n = FnFn+1 1. Use induction to prove that 1 3+2³+3³+ +n³ = n² (n + 1)² /4 for all integers n ≥ 1. 2. Use induction to prove that the following identity holds for all integers n ≥ 1:1+3+5++ (2n-1) = n 2. Exercises 3.5 1. Use induction to prove that n(n + 1)(n + 2) is a multiple of 3 for all integers n ≥ 1. 2. Use induction to show that n³ + 5n s a multiple of 6 for any nonnegative integer n. Exercises 3.6 1. Use mathematical induction to prove the identity F 21+F22+F23+ · · · + for any integer n ≥ 1. ++ F2n = FnFn+1

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i Let us prove that nn1 nn1 for all positive 4 integers ... View the full answer