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(4) A Fibonacci-like sequence Gk is constructed by setting G0 = 0, G1 = 1, and…
(4) A Fibonacci-like sequence Gk is constructed by setting G0 = 0, G1 = 1, and Gk+2 = 1 2 (Gk+1 + Gk). (a) Find a matrix A so that Gk+2 Gk+1 = A Gk+1 Gk . (b) Diagonalize A and find a formula of Ak in terms of k. (c) Use this to find a formula for Gk. (d) Find limk→∞ Gk.
(4) A Fibonacci-like sequence Gk is constructed by setting Go 0, G1 1, and Gk+2(GkG a) Find a matrix A so that k2A (b) Diagonalize A and find a formula of A* in terms of k (c) Use this to find a formula for Gk. (d) Find limkGk
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