Question: Solution to recursively defined sequence Given the sequence an defined recursively as - a0=1 - a1=1 - ak=4ak2 for every integer k>1 You will now

Solution to recursively defined sequence Given the sequence an defined recursively as - a0=1 - a1=1 - ak=4ak2 for every integer k>1 You

Solution to recursively defined sequence Given the sequence an defined recursively as - a0=1 - a1=1 - ak=4ak2 for every integer k>1 You will now prove by strong induction that the solution for this sequence is - an=412n+43(2)n The conjecture that you are proving, is expressed symbolically in the form nD,P(n). - (1 mark) What is the set D? - (1 mark) What is the predicate function P(n) in symbolic form? Base Cases (3 marks) Prove your base cases 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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