Alternating Series
Definition
An alternating series is a series in which the signs of the terms alternate between positive and negative.
Analogy
Imagine a game where you earn or lose points based on whether you win or lose each round. In an alternating series, it's like gaining points for winning a round and losing points for losing a round, with the signs of the points alternating.
Related terms
Convergence: The property of a series that means it approaches a finite value as more terms are added.
Divergence: The property of a series that means it does not approach any finite value as more terms are added.
Absolute Convergence: A type of convergence where both the original series and its absolute value converge to finite values.
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Additional resources (1)
Practice Questions (9)
What form do terms of an alternating series have?
For an alternating series, if the error bound is 0.032, what can you say about the approximation?
What is the error bound for the alternating series with the first term (-1)^n/n^2 and n terms given by the series sum (1/n^2)?
For the alternating series (-1)^n/(2n+1), what is the error bound for the approximation obtained by using the first 5 terms?
What is the error bound for the alternating series (-1)^n/n!, when approximated using the first 4 terms?
How does the error bound change if the terms of an alternating series converge to zero more quickly?
For the alternating series (-1)^n*(n^2 + 1)/(n^3 + 3), what is the error bound for the approximation obtained by using the first 2 terms?
For the alternating series (-1)^n/(n^3 + 1), what is the error bound for the approximation obtained by using the first 3 terms?
What is the error bound for the alternating series (-1)^n/(3n^2 - 2n), when approximated using the first 6 terms?
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