Given the sequence b defined recursively as follows: b = bk = bk-1 1+2bk-1 when k>1...

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Given the sequence b defined recursively as follows: b = bk = bk-1 1+2bk-1 when k>1 1 Prove using mathematical (weak) induction that for values of n greater or equal to 1, b = = 2n Before you start you will need to translate this theorem in symbolic form, in the form of VnED, P(n) 1. Set D (1 mark) What is the set D in the symbolic form VnED, P(n) of the theorem you will prove? 2. P(n) (2 marks) What is the predicate function P(n) in the symbolic form VnED, P(n) of the theorem you will prove? You will now prove the theorem by induction. No other method is acceptable. Be sure to lay out your proof clearly and correctly and to justify every step. 3. Proof: Base Case(s) (2 marks) Write the base case(s) of your proof here. 4. Proof: Inductive Step Setup (4 marks) This is the beginning of the inductive step where you are stating the assumptions in the inductive step and what you will be proving in that step. As you do so, identify the inductive hypothesis. 5. Proof: Inductive Step (6 marks) Write the remainder of the inductive step of your proof here. Justify every step. Given the sequence b defined recursively as follows: b = bk = bk-1 1+2bk-1 when k>1 1 Prove using mathematical (weak) induction that for values of n greater or equal to 1, b = = 2n Before you start you will need to translate this theorem in symbolic form, in the form of VnED, P(n) 1. Set D (1 mark) What is the set D in the symbolic form VnED, P(n) of the theorem you will prove? 2. P(n) (2 marks) What is the predicate function P(n) in the symbolic form VnED, P(n) of the theorem you will prove? You will now prove the theorem by induction. No other method is acceptable. Be sure to lay out your proof clearly and correctly and to justify every step. 3. Proof: Base Case(s) (2 marks) Write the base case(s) of your proof here. 4. Proof: Inductive Step Setup (4 marks) This is the beginning of the inductive step where you are stating the assumptions in the inductive step and what you will be proving in that step. As you do so, identify the inductive hypothesis. 5. Proof: Inductive Step (6 marks) Write the remainder of the inductive step of your proof here. Justify every step.