4. n→∞ (a) Give an example of a convergent sequence (an) of positive numbers with lim x/n = 1. (b) Give an example of a

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4 N A Give An Example Of A Convergent Sequence An Of Positive Numbers With Lim X N 1 B Give An Example Of A 1 (58.42 KiB) Viewed 43 times

4. n→∞ (a) Give an example of a convergent sequence (an) of positive numbers with lim x/n = 1. (b) Give an example of a divergent sequence (n) of positive numbers with lim x/n = 1. n→∞ (c) Give an example of a convergent sequence (an) of positive numbers with lim = 1. Xn+1 n→∞ In Xn+1 84x In (d) Give an example of a divergent sequence (n) of positive numbers with lim = 1. (e) Determine whether the statements given below are true/false: i. If (n) is any sequence of positive numbers with lim x¹/n gent. = 1, then (n) is conver- 'n n→∞ Xn+1 ii. If (n) is any sequence of positive numbers with lim = 1, then (n) is con- n→∞ Xn vergent.