Question

What is the quickest way to show that a sequence does not converge?

A. Showing that it is bounded.
B. Showing that it is unbounded.
C. Showing that it is monotonic.
D. Showing that it is periodic.

Answer 1

The quickest way to show that a sequence does not converge is to show that it is unbounded.

Step-by-step explanation:

The quickest way to show that a sequence does not converge is to show that it is unbounded. If a sequence is unbounded, it means that the terms of the sequence become larger and larger without limit. This indicates that the sequence does not approach a fixed value and therefore does not converge.

For example, consider the sequence {1, 2, 3, 4, 5, ...}. This sequence is unbounded because the terms continue to increase without bound.

If the sequence is bounded, this does not necessarily imply that it converges. A bounded sequence means that all the terms of the sequence are within a certain range, but it may still oscillate or not approach a fixed value.