Use mathematical induction to prove that the statements are true for every positive integer n. n (n+1) n (n+1)(n+2) (a) 1+3+6+..+ 2 Sn (n+1) (b) 5+ 10 + 15 +...+ 5n = 2 (c) 12 + 23+...+n³ = n²(n+1)? 4...

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Extracted text: Use mathematical induction to prove that the statements are true for every positive integer n. n (n+1) n (n+1)(n+2) (a) 1+3+6+..+ 2 Sn (n+1) (b) 5+ 10 + 15 +...+ 5n = 2 (c) 12 + 23+...+n³ = n²(n+1)? 4 (d) 14 + 24+.., +n' = n (n+1)(2n+1) (3n? +3n-1) %3D 30 (e) 1+ a+ a? +..+ a"-1 = for a + 0, a + 1 () 32n +7 is divisible by 8 (g) 13" + 6" is divisible by 7 (h) 25n+1 + 52n+2 is divisible by 27 (i) 72n + 16n – 1 is divisible by 64 - n is divisible by 3 G) na