3-14 - Proving a Formula Use mathematical induction to prove that the formula is true for all natural numbers n. 3. 2 + 4 + 6 + · .. + 2n = n(n + 1) n(3n – 1) 4. 1+ 4 +7+ .. + (3n – 2) = 2 п(Зл + 7) 5. 5 + 8+ 11 + ... + (3n + 2) = 2 n(n + 1)(2n + 1) .. + n° 6. 12 + 22 + 3? + 6. n(n + 1)(n + 2) 7. 1.2 + 2.3 + 3.4 +... + n(n + 1) = 3 п(п + 1)(2л + 7) 8. 1.3 + 2.4 + 3.5 +. + n(n + 2) = 6. n°(n + 1)? 9. 1 + 2 + 3 + -.+ n = 4 – 1)° = n°(2n² – 1) + ...+ (2n) = 2n°(n + 1)? 10. 1' + 3 + 5° + -..+ (2n 11. 2 + 4' + 6' 12. 1.2 n(n + 1) (п + 1) 2.3 3.4 13. 1.2 + 2.22 + 3.2 + 4.2* + -.. + n- 2" = 2[1 + (n – 1)2"] 14. 1 + 2 + 2 + -..+ 2"-1 = 2" – 1 + +

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