Chapter 4: 4.6.8, 4.6.9 (a),(b), 4.6. (b), (c), 4.6.14 1. Prove that for any natural n the following holds (n- 1)n(n+ 1) 1.2+2.3+...+ (n - 1) n = 3. 2. Prove that for any natural n the following holds...

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Extracted text: Chapter 4: 4.6.8, 4.6.9 (a),(b), 4.6. (b), (c), 4.6.14 1. Prove that for any natural n the following holds (n- 1)n(n+ 1) 1.2+2.3+...+ (n - 1) n = 3. 2. Prove that for any natural n the following holds 1 1 1 1 ... 1.3 3.5 5-7 (2n - 1)(2n + 1) 2n +1 3. Multiply out i writing the result in summation notation. i-1 4. For the inequality 3"+1>n determine the set of natural numbers for which it