Question

Determine if each sequence converges or diverges. Find the limit of any convergent sequences.

Answer 1

Convergent and divergent sequences

Step-by-step explanation:

In mathematics, we use the terms 'converge' and 'diverge' to describe the behavior of sequences. A sequence converges if its terms approach a specific limit as the sequence progresses. On the other hand, a sequence diverges if it does not approach a limit.

To determine if a sequence converges or diverges, we need to analyze its behavior. This can be done by finding the limit of the sequence. If the limit exists, the sequence converges. If the limit does not exist, the sequence diverges.

Here are the steps to determine if a sequence converges or diverges:

1. Compute the terms of the sequence.
2. Observe the behavior of the terms as the sequence progresses.
3. If the terms approach a specific limit, the sequence converges.
4. If the terms do not approach a specific limit, the sequence diverges.