Suppose {x_n}^infinity _n=0 is a sequence that converges to p, with x_n p for al

Question

Suppose {x_n}^infinity _n=0 is a sequence that converges to p, with x_n p for all n. If positive constants lambda and alpha exist with then {x_n}^infinity _n=0 converges to p of order alpha. For each of the following sequences, select your answer out of the given choices. What is the order of convergence for the sequence {10^-3n} infinity _n=0 to 0? What is the order of convergence for the sequence {10^-3^n} infinity _n=0 to 0? Linear convergence (i.e. alpha = 1) Quadratic convergence (i.e. alpha = 2) Cubic convergence (i.e. alpha = 3) None of the above

Explanation / Answer

solution 1)order of convergence for the sequence is cubic convergence. solution 2)order of convergence for the sequence is none of the above.

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