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.

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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

11.J. If X
and equals a number less than 1, then lim Y
with ) <r < 1 and some A > 0, then 0 < Xn < Ar" for sufficiently large n.)
11.K. If, in Exercise 11.J. the sequence (1/xn) 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)
(xn) is a sequence of positive numbers and if lim (xn+1/xn) exists
0. (Hint: show that for some r
(Xn) of positive numbers with
0. Also give an example of a divergent
= 1 and such that lim X
1.

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