Series | Alternating Series Test (with Conditional/Absolute Convergence): Examples 1 & 2

The video tutorial explains the alternating series test, providing an example series to illustrate the test's criteria for convergence. It discusses the two main criteria: the limit of B sub N must be zero, and B sub N must be decreasing. The tutorial then differentiates between conditional and absolute convergence, using the harmonic series as an example. A second example is provided to show a case where the test is inconclusive, leading to a discussion on divergence.

What is the first step in determining if a series is alternating?

• Check if the series is geometric

• Write out the first few terms to observe sign changes

• Determine if the series is harmonic

• Calculate the sum of the series

What must be true for the limit of B sub N in an alternating series test?

• It must be less than 0

• It must equal 0

• It must be greater than 1

• It must equal 1

What does it mean if the absolute value of a series diverges?

• The series is conditionally convergent

• The series is geometric

• The series is absolutely convergent

• The series is divergent

What is the result if the first criterion of the alternating series test fails?

• The test is inconclusive

• The series automatically converges

• The series is conditionally convergent

• The series automatically diverges

What should be done if the alternating series test is inconclusive?

• Use the test for convergence

• Assume the series converges

• Use the test for divergence

• Assume the series diverges

What happens to the limit of an alternating term as N approaches infinity?

• It becomes infinite

• It becomes zero

• It oscillates between two values

• It settles on a single value

What is the significance of a divergent limit in the context of the alternating series test?

• It indicates absolute convergence

• It indicates conditional convergence

• It suggests the series does not settle on a single value

• It confirms the series is geometric