1. This question refers to the following recurrence relation. 1, T(n) = { } }(n n...
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1. This question refers to the following recurrence relation. 1, T(n) = { } }(n n = 1 T(n-1)+2n-1, n >1 (a) [2 marks] Assume that n is much larger than 1. Use the recurrence relation to write T(n) in terms of T(n - 1), then in terms of T(n 2), and finally in terms of T(n 3). You can perform more substitutions if you wish in order to see the pattern. - (b) [2 marks] Conjecture an expression for T(n) in terms of T(n - j), for an arbitrary j. Your expression can involve summation notation. For what range of j values does your conjecture apply? (c) [2 marks] Using part (b), conjecture a closed-form solution for T(n) as a function of n. Evaluate any summation notation. (d) [3 marks] Prove your conjecture using mathematical induction. Activate Windows Go to Settings to activate Windo 1. This question refers to the following recurrence relation. 1, T(n) = { } }(n n = 1 T(n-1)+2n-1, n >1 (a) [2 marks] Assume that n is much larger than 1. Use the recurrence relation to write T(n) in terms of T(n - 1), then in terms of T(n 2), and finally in terms of T(n 3). You can perform more substitutions if you wish in order to see the pattern. - (b) [2 marks] Conjecture an expression for T(n) in terms of T(n - j), for an arbitrary j. Your expression can involve summation notation. For what range of j values does your conjecture apply? (c) [2 marks] Using part (b), conjecture a closed-form solution for T(n) as a function of n. Evaluate any summation notation. (d) [3 marks] Prove your conjecture using mathematical induction. Activate Windows Go to Settings to activate Windo
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Related Book For
Applied Regression Analysis and Other Multivariable Methods
ISBN: 978-1285051086
5th edition
Authors: David G. Kleinbaum, Lawrence L. Kupper, Azhar Nizam, Eli S. Rosenberg
Posted Date:
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