Prove the below equations by induction (b) (1) (2)+(2)(3) ++ (n)(n+1)= 1 (c) (n)(n+1) 1 n (2n-1)(2n
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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
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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