Final answer:
To determine if a sequence converges or diverges, analyze its behavior as the terms continue. Look for patterns, calculate the limit, or use convergence tests. Example: {1, 1/2, 1/4, 1/8, ...} converges to 0.
Step-by-step explanation:
To determine if a sequence converges or diverges, we can analyze its behavior as the terms of the sequence continue. If the terms of the sequence approach a particular number as the sequence goes on, the sequence is said to converge. On the other hand, if the terms of the sequence do not approach a specific number and instead get infinitely large or fluctuate, the sequence is said to diverge.
To analyze the behavior of a sequence, you can look for patterns, calculate the limit of the sequence, or use convergence tests such as the limit comparison test, ratio test, or the root test. These tests evaluate the behavior of the sequence and determine if it converges or diverges.
For example, if we have the sequence {1, 1/2, 1/4, 1/8, ...}, we can see that the terms of the sequence are getting smaller and approaching 0. In this case, the sequence converges to 0.