Question

Given: For both of the following answer blanks, decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit (for a sequence) or the sum (for a series).

a. Convergent; [infinity]
b. Divergent
c. Convergent; 1
d. Divergent

Answer 1

Convergent and divergent series are terms used to describe the behavior of infinite sequences or series. A convergent sequence or series has a clear limit or sum, while a divergent sequence or series does not.

Step-by-step explanation:

Convergent and divergent series are terms used to describe the behavior of infinite sequences or series. A convergent sequence or series has a clear limit or sum, while a divergent sequence or series does not.

In the given options, a is labeled as convergent with a limit of infinity. This means that the sequence associated with option a is increasing without bound. Option b is labeled as divergent, indicating that the associated series does not have a clear sum. Option c is convergent with a sum of 1. Lastly, option d is divergent, meaning that the series associated with it does not have a clear sum.