Find closed forms for each of the following recurrences. (a) F(n) = F(n − 1) + 3; F(1) = 2. (b) F(n) = 2F(n − 1); F(0) = 1. (c) F(n) = 2F(n − 1) + 1; F(1) = 1. (d) F(n) = 2nF(n − 1); F(0) = 1. (e)...

Find closed forms for each of the following recurrences.

(a) F(n) = F(n − 1) + 3; F(1) = 2.

(b) F(n) = 2F(n − 1); F(0) = 1.

(c) F(n) = 2F(n − 1) + 1; F(1) = 1.

(d) F(n) = 2nF(n − 1); F(0) = 1.

(e) F(n) = 2nF(n − 1); F(0) = 1.

(f) F(n) = 2 + Pn−1i=1 F(i); F(1) = 1.

Find Θ for each of the following recurrence relations.

(a) T(n) = 2T(n/2) + n².

(b) T(n) = 2T(n/2) + 5.

(c) T(n) = 4T(n/2) + n.

(d) T(n) = 2T(n/2) + n².

(e) T(n) = 4T(n/2) + n³.

(f) T(n) = 4T(n/3) + n.

(g) T(n) = 4T(n/3) + n².

(h) T(n) = 2T(n/2) + log n.

(i) T(n) = 2T(n/2) + n log n.