Question

Find an example of a sequence, {xn}, that does not converge, but has a convergent subsequence....

Find an example of a sequence, {xn}, that does not converge, but has a convergent subsequence. Explain why {xn} (the divergent sequence) must have an infinite number of convergent subsequences.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

12

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove that every bounded sequence has a convergent subsequence.
Prove that every bounded sequence has a convergent subsequence.
Show that sequence {sn} converges if it is monotone and has a convergent subsequence.
Show that sequence {sn} converges if it is monotone and has a convergent subsequence.
Suppose that every Cauchy sequence of X has a convergent subsequence in X. Show that X...
Suppose that every Cauchy sequence of X has a convergent subsequence in X. Show that X is complete.
Prove that X is totally bounded if every sequence of X has a convergent subsequence. Please...
Prove that X is totally bounded if every sequence of X has a convergent subsequence. Please directly prove it without using any theorem on totally boundedness.
Find a sequence of positive Lebesgue integrable functions on [0,1] which do not converge pointwise (it...
Find a sequence of positive Lebesgue integrable functions on [0,1] which do not converge pointwise (it means that there is no point x0 so that fn(x0 ) is a convergent sequence) but its integrals do converge to zero.
4.2.7. Example. If (xn) is a sequence in (0, ∞) and xn → a, then √xn...
4.2.7. Example. If (xn) is a sequence in (0, ∞) and xn → a, then √xn → √a. ? Proof. Problem. Hint. There are two possibilities: treat the cases a = 0 and a > 0 sepa- √√ rately. For the first use problem 4.1.7(a). For the second use 4.2.1(b) and 4.1.11; write xn − a as |xn − a|/(√xn + √a). Then find an inequality that allows you to use the sandwich theo- rem(proposition 4.2.5).
Determine whether the following sequences converge or diverge. If a sequence converges, find its limit. If...
Determine whether the following sequences converge or diverge. If a sequence converges, find its limit. If a sequence diverges, explain why. (a) an = ((-1)nn)/ (n+sqrt(n)) (b) an = (sin(3n))/(1- sqrt(n))
Prove that the sequence cos(nπ/3) does not converge. let epsilon>0 find a N so that |An|...
Prove that the sequence cos(nπ/3) does not converge. let epsilon>0 find a N so that |An| < epsilon for n>N
find the nth term of the following sequence, does it converge? {2/1, 6/10, 12/100, 60/1000....}
find the nth term of the following sequence, does it converge? {2/1, 6/10, 12/100, 60/1000....}
construct an example of sequence of functions that the family of such function is uniformly bounded...
construct an example of sequence of functions that the family of such function is uniformly bounded but does not have subsequence that converges uniformly, with detail proof.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT