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Prove that the correctness of the following properties of the given recursive sequences. a) Given the...

Prove that the correctness of the following properties of the given recursive sequences.

a) Given the sequence P(1) = 1, P(n) = 2∗P(n−1) for all n ≥ 1, prove that P(n) = 2n−1 for all n ≥ 1

b) Given the sequence P(1) = 1, P(2) = 1, P(3) = 1, P(4) = 1, P(n) = P(n − 2) + P(n − 4) for all n ≥ 5, prove that P(n) = P(n − 1) for all even positive integers n.

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