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.
Added by Jason M.
Step 1
This sequence does not converge because it oscillates between -1 and 1 indefinitely. However, it has a convergent subsequence. For example, the subsequence {x2n} = (-1)^(2n) = 1 for all n, which clearly converges to 1. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Sri K and 58 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
State Bolzano Weierstrass Theorem. Give an example of an infinite sequence of distinct terms {xn} such that {xn} is bounded, {xn} is not monotone and {xn} has a convergent subsequence {xni}
Madhur L.
3. Give examples of: (a) An unbounded sequence with no convergent subsequences (b) An unbounded sequence with exactly one subsequential limit (c) An unbounded sequence with exactly two subsequential limits (Here, subsequential limit means what you think it should: the limit of some subse- quence of an. Ask if it isn't clear!)
Shaiju T.
Give an example of a bounded sequence that is not convergent.
Sequences and Series
Monotonic Sequences
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
600,000+
Students learning Calculus with Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD
