Prove the below equations by induction (b) (1) (2)+(2)(3) ++ (n)(n+1)= 1 (c) (n)(n+1) 1 n (2n-1)(2n

Prove the below equations by induction

 

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(b) (1) (2)+(2)(3) ++ (n)(n+1)= 1 (c) (n)(n+1) 1 n (2n-1)(2n + 1) 2n +11 1 1 + (1)(2) (2) (3) 1 1 (d) (1)(3) (3)(5) (e) n² +n is divisible by 2 (Can you prove this directly?); (f) n³+2n is divisible by 3: 3; (g) an-bn is divisible by a - b (Hint: Show that a+bk+1 = ak(a - b) + b(a - b)). + + n(n + 1)(n + 2) 3 + H = n+1 C (b) (1) (2)+(2)(3) ++ (n)(n+1)= 1 (c) (n)(n+1) 1 n (2n-1)(2n + 1) 2n +11 1 1 + (1)(2) (2) (3) 1 1 (d) (1)(3) (3)(5) (e) n² +n is divisible by 2 (Can you prove this directly?); (f) n³+2n is divisible by 3: 3; (g) an-bn is divisible by a - b (Hint: Show that a+bk+1 = ak(a - b) + b(a - b)). + + n(n + 1)(n + 2) 3 + H = n+1 C

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b To prove the equation 12 23 nn 1 nn 1n 23 by induction Base Case For n 1 the lefthand side is 12 and the righthand side is 11 11 23 23 The base case holds Inductive Step Assume that the equation hol... View the full answer