Question 2 Consider the following recursively defined function F: N → N: F(n) = = if n = 0 if n>0 CF(i) In other words, F(n) for n ≥ 1 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) = 2n-¹? (c.) Prove by induction over n that F(n) 2n-1 for n ≥ 1.

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