2. Use mathematical induction to prove that the statements are true for every positive integer n. (a) 1+3+6+...+ n (n+1) n (n+1)(n+2) 2 (b) 5+ 10 + 15 +...+ 5n = Sn (n+1) (c) 12 + 23+...+n³ = n°(n+1)²...

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2. Use mathematical induction to prove that the statements are true for every positive integer n.<br>(a) 1+3+6+...+<br>n (n+1)<br>n (n+1)(n+2)<br>2<br>(b) 5+ 10 + 15 +...+ 5n =<br>Sn (n+1)<br>(c) 12 + 23+...+n³ = n°(n+1)²<br>(d) 14 + 24+...+ n° = n(n+1)(2n+1) (3n² +3n-1)<br>30<br>(e) 1+a+ a? +...+ a

Extracted text: 2. Use mathematical induction to prove that the statements are true for every positive integer n. (a) 1+3+6+...+ n (n+1) n (n+1)(n+2) 2 (b) 5+ 10 + 15 +...+ 5n = Sn (n+1) (c) 12 + 23+...+n³ = n°(n+1)² (d) 14 + 24+...+ n° = n(n+1)(2n+1) (3n² +3n-1) 30 (e) 1+a+ a? +...+ a"-1 a"- %3D for a + 0, a + 1 a-1

Jun 04, 2022

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2. Use mathematical induction to prove that the statements are true for every positive integer n. (a) 1+3+6+...+ n (n+1) n (n+1)(n+2) 2 (b) 5+ 10 + 15 +...+ 5n = Sn (n+1) (c) 12 + 23+...+n³ = n°(n+1)²...

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