17. (a) (b) Give an example of a convergent sequence (x) of positive numbers with lim(x+1/xn) = 1. Give an example of a divergent sequence with this property. (Thus, this property cannot be used as a test for convergence.)

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17. (a)
(b)
Give an example of a convergent sequence (x) of positive numbers with lim(x+1/xn) = 1.
Give an example of a divergent sequence with this property. (Thus, this property cannot be
used as a test for convergence.)
Transcribed Image Text:17. (a) (b) Give an example of a convergent sequence (x) of positive numbers with lim(x+1/xn) = 1. Give an example of a divergent sequence with this property. (Thus, this property cannot be used as a test for convergence.)
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