Does Every Unbounded Sequence Divergent?

Every unbounded sequence is divergent. The sequence is monotone increasing if a n ≤ a n + 1 for every. Similarly, the sequence is called monotone decreasing if a n ≥ a n + 1 for every. The sequence is called monotonic if it is either monotone increasing or monotone decreasing.

Can unbounded sequence converge?

So unbounded sequence cannot be convergent.

Do unbounded sequences have convergent subsequences?

(a) An unbounded sequence has no convergent subsequences. ... Since (ank ) is a bounded sequence, it has a convergent subsequence by the Bolzano-Weierstrass Theorem. This convergent subsequence is a subsequence of the original sequence by problem 2. Thus the contrapositive of statement (b) is true.