What is an unbounded sequence?

Published by Charlie Davidson on

What is an unbounded sequence?

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. Then it is not bounded above, or not bounded below, or both.

What is a monotone sequence?

Monotone Sequences. Definition : We say that a sequence (xn) is increasing if xn ≤ xn+1 for all n and strictly increasing if xn < xn+1 for all n. Similarly, we define decreasing and strictly decreasing sequences. Sequences which are either increasing or decreasing are called monotone.

What is a bounded sequence in calculus?

A sequence is bounded if it is bounded above and below, that is to say, if there is a number, k, less than or equal to all the terms of sequence and another number, K’, greater than or equal to all the terms of the sequence. Therefore, all the terms in the sequence are between k and K’.

What is Convergent sequence in calculus?

A convergent sequence has a limit — that is, it approaches a real number. A divergent sequence doesn’t have a limit. Here’s an example of a convergent sequence: This sequence approaches 0, so: Thus, this sequence converges to 0.

What is monotone sequence give example?

A sequence is said to be monotone if it is either increasing or decreasing. The sequence n2 : 1, 4, 9, 16, 25, 36, 49, is increasing. The sequence 1/2n : 1/2, 1/4, 1/8, 1/16, 1/32, is decreasing.

What is a divergent sequence give two examples?

Mathwords: Divergent Sequence. A sequence that does not converge. For example, the sequence 1, 2, 3, 4, 5, 6, 7, diverges since its limit is infinity (∞). The limit of a convergent sequence must be a real number.

How do you tell if a function diverges or converges?

convergeIf a series has a limit, and the limit exists, the series converges. divergentIf a series does not have a limit, or the limit is infinity, then the series is divergent. divergesIf a series does not have a limit, or the limit is infinity, then the series diverges.

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