Consider the following recursively defined function F: NN: if n = 0 if n > 0...

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Consider the following recursively defined function F: N→N: if n = 0 if n > 0 F(n) = {-- F(i) In other words, F(n) for n 21 is defined as the sum of all previous values of F. (a.) Show the values of F(0), F(1), F(2), F(3), F(4), F(5) and how to compute them using the definition above. (b.) For which of the F(0),..., F(5) do we have that F(n) = 2"-¹? (c.) Prove by induction over n that F(n) = 2"-1 for n ≥ 1. Consider the following recursively defined function F: N→N: if n = 0 if n > 0 F(n) = {-- F(i) In other words, F(n) for n 21 is defined as the sum of all previous values of F. (a.) Show the values of F(0), F(1), F(2), F(3), F(4), F(5) and how to compute them using the definition above. (b.) For which of the F(0),..., F(5) do we have that F(n) = 2"-¹? (c.) Prove by induction over n that F(n) = 2"-1 for n ≥ 1.

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a The values of F0 F1 F2 F3 F4 F5 and how to compute them using ... View the full answer