1. Give an example of an unbounded sequence that does not diverge to + or to – . 2. (a) Give an example of a convergent sequence (sn) of positive numbers such that lim (sn+1/sn) = 1. (b) Give an...

1. Give an example of an unbounded sequence that does not diverge to +

or to –
.

2. (a) Give an example of a convergent sequence (s_n) of positive numbers such that lim (s_n+1/s_n) = 1.

(b) Give an example of a divergent sequence (t_n) of positive numbers such that lim (t_n+1/t_n) = 1.

3. Let (s_n) be a sequence of positive terms such that the sequences of ratios (s_n
+ 1/s_n) converges to L. Prove that if L > 1, then lim s_n
= +
.