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4. Let an be the sequence defined by a0 = 0 and an = 2an−1 +...

4.

Let an be the sequence defined by a0 = 0 and an = 2an−1 + 2 for n > 1.

(a) Find the value of sum 4 i=0 ai .

(b) Use induction to prove that an = 2n+1 − 2 for all n ∈ N.

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