Chapter 4: 4.6.8, 4.6.9 (a),(b), 4.6.11 (b), (c), 4.6.14 1. Prove that for any natural n the following holds 1.2+2.3+...+ (n– 1) n D (п - 1)п(п + 1) 3 2. Prove that for any natural n the following...

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Extracted text: Chapter 4: 4.6.8, 4.6.9 (a),(b), 4.6.11 (b), (c), 4.6.14 1. Prove that for any natural n the following holds 1.2+2.3+...+ (n– 1) n D (п - 1)п(п + 1) 3 2. Prove that for any natural n the following holds 1 1 1 1.3 3.5 5-7 (2n 1)(2n + 1) 2n + 1 3. Multiply out Ti writing the result in summation notation. i-1 4. For the inequality 3"+1 >n determine the set of natural numbers for which it hol