Alternating Series Test
Definition
The alternating series test is used to determine whether an alternating series converges by checking if its terms satisfy certain conditions involving decreasing magnitude and approaching zero.
Analogy
Imagine you're playing Jenga, where each block represents a term in an alternating series. If each block gets smaller and smaller, and eventually becomes so small that you can't even see it anymore, then your tower will be stable and converge. But if any block starts getting bigger again, your tower will collapse and diverge.
Related terms
Alternating Series: A series whose terms alternate between positive and negative values.
Absolute Convergence: A type of convergence where both positive and negative terms in a series converge individually.
Conditional Convergence: A type of convergence where rearranging the order of terms in a convergent series can change its sum.
"Alternating Series Test" appears in:
Additional resources (1)
Practice Questions (8)
What is the Alternating Series Test used for?
Which series can be tested for convergence or divergence using the Alternating Series Test?
What is the main condition for the Alternating Series Test to be applicable?
What does the Alternating Series Test conclude when the terms of an alternating series do not approach zero?
Which of the following series converges according to the Alternating Series Test?
Which of the following series diverges according to the Alternating Series Test?
Which of the following series converges conditionally according to the Alternating Series Test?
Which of the following series cannot be tested using the Alternating Series Test?
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