Submit your solutions to the following problems: 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 (п — 1)п (п + 1) 1.2 + 2 ·3 + ...+ (n – 1)...

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Extracted text: Submit your solutions to the following problems: 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 (п — 1)п (п + 1) 1.2 + 2 ·3 + ...+ (n – 1) · n = 3 2. Prove that for any natural n the following holds 1 1 .. + (2n – 1)(2n + 1) 1. 3 3-5 5-7 2n + 1 2 3. Multiply out Σ writing the result in summation notation. i=1 4. For the incquality 3"+1> n° determine the set of natural numbers for which it holds.