Answer: In 15 through 18 we indicate how to prove that the sequence {n(t)}, defined by
Chapter 2, Problem 18(choose chapter or problem)
In 15 through 18 we indicate how to prove that the sequence {n(t)}, defined by Eqs. (4) through (7), converges.Note thatn(t) = 1(t) + [2(t) 1(t)]++[n(t) n1(t)].(a) Show that|n(t)||1(t)|+|2(t) 1(t)|++|n(t) n1(t)|.(b) Use the results of to show that|n(t)| MKKh + (Kh)22! ++ (Kh)nn!.(c) Show that the sum in part (b) converges as n and, hence, the sum in part (a)also converges as n . Conclude therefore that the sequence {n(t)} converges sinceit is the sequence of partial sums of a convergent infinite series.
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