Determine the limit of the sequence or show that it diverges; (use the squeeze theorem). b_n = 9^n / n!. Determine whether the sequence given below is monotonic or not. Also, determine whether the given sequence is bounded or u...
Determine whether the sequence is monotonic or eventually monotonic, and whether the sequence is bounded above and/or below. If the sequence converges, give the limit. Given the sequence a_n = \frac{sin(4n)}{n^6 + 3}: Is this sequence Bounde...
The answer is yes. By definition an unbounded sequence is a sequence that it is not bounded. Upvote • 0 Downvote Add comment Still looking for help? Get the right answer, fast. Ask a question for free Get a free answer to a quick problem. Most questions answered ...
The simplest way to analyze convergence is to see whether the sequence is bounded or not. If the sequence is not bounded, then it's definitely divergent. However, this does not imply that every bounded sequence is convergent. The question of when does a sequence converge (in the case of ...
As we saw in the last chapter, when we graph several terms of a sequence, certain behavior may appear. We may become convinced, for whatever reason, that the sequence is unbounded. Or, we may believe that the sequence is bounded and we may even notice the sequence moving toward a ...
We're given the series ##\sum_{n=1}^{\infty} [ \sqrt{n+1} - \sqrt{n} ]##. ##s_n = \sqrt{n+1} - 1## ##s_n## is, of course, an increasing sequence, and unbounded, given any ##M \gt 0##, we have ##N = M^2 +2M## such that ##n \gt N \implies s_n ...
The sequence is considered monotone if the sequence is increasing or the sequence is decreasing continousily .We may calculate the ratio of the two successive termsanandan+1to check the sequence monotonicity. The monotone sequence could be bounded ...
How do you prove a sequence is not bounded? If a sequence is not bounded,it is an unbounded sequence. For example, the sequence 1/n is bounded above because 1/n≤1 for all positive integers n. It is also bounded below because 1/n≥0 for all positive integers n. Therefore, 1/n is...
has bounded geometry. In this section we further assume that the sequence has ANSC with essential origins. 3 2.2 The four types of sequences We shall categorize the types of sequences by whether they have bump-like or split-like origins and whether the diameters are bounded or unbounded....
We term {D^k(n)}_{k >= 0} the derived sequence of n. We show that all derived sequences of n < 1.5 * 10^10 are bounded, and that the density of those n in N with bounded derived sequences exceeds 0.996, but we conjecture nonetheless the existence of unbounded sequences. Known...