11.J. If X and e quals a number less than 1, then lim X = with ) 0, then 0 < xn < Ar" for sufficiently large n.) 11.k. If, in Exercise 11.J. the sequence (rn+1/In) converges to a number greater than 1, then the sequence .X does not converge, 11.L. Give an example of a sequence X lim (1n+1/xn) sequence X such that lim (xn+1/Xn) (rn) is a sequence of positive numbers and if lim (xn+1/xn) exists 0. (Hint: show that for some r (In) of positive numbers with = 1 and such that lim X = 0. Also give an example of a divergent = 1.

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