Question: Now prove by mathematical induction that the solution that you guessed for the sequence in previous question is correct. Solution to recursively defined sequence Given

Now prove by mathematical induction that the solution that you guessed for the sequence in previous question is correct.

Solution to recursively defined sequence Given the sequence an defined recursively as - a1=21 - ak=ak1+k(k+1)1 for every integer k>1 You will now use iteration to guess a solution for this sequence: 1. Calculate a2,a3,a4. Show all the steps in your derivations. Your answers should be in the form of simplified fractions. 2. Based on this pattern, guess an analytical solution for this sequence. Problem Statement ( 3 marks) The conjecture that you are proving, is expressed symbolically in the form nD,P(n). - (1 mark) What is the set D ? - (2 mark) What is the predicate function P(n) in symbolic form? Base Case (2 marks) Prove your base case here Inductive Step (10 marks) a) Inductive step setup. - (2 marks) State the assumption in the inductive step and identify the inductive hypothesis. - (2 marks) State what you will be proving in the inductive step. b) Remainder of Inductive step ( 6 marks). Finish your proof here. Be sure to justify every step. particularly why the inductive hypothesis and recursive definitions can be applied

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StepbyStep Solution Calculating a2 a3 a4 Calculate a2 a2 a1 frac1221 a2 frac12 frac16 frac36 frac16 ... View full answer

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