The alternating series estimation theorem to estimate the value of the series and state the error — Krista King Math | Online math help
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The alternating series estimation theorem to estimate the value of the series and state the error — Krista King Math | Online math help
The alternating series estimation theorem gives us a way to approximate the sum of an alternating series with a remainder or error that we can calculate. To use the theorem, the alternating series must follow two rules.
May 16, 2019
Alternating series test Definition
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Geometric series test to figure out convergence — Krista King Math | Online math help
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SOLVED: Theorem 2.7.7 (Alternating Series Test). Let (an) be a sequence satisfying a1 >= a2 >= a3 >= ... >= 0. Then, the alternating series Σ((-1)^n * an) converges.Proof: The conditions of this theorem are outlined in Exercise 2.7.1. One consequence of these conditions is that an >= 0 for all n. Several proofs of Definition 2.7.8 - Convergence of a Series are given in Exercise 2.7.1.Exercises Exercise 2.7.1. Proving the Alternating Series Test (Theorem 2.7.7) amounts to showing that the sequen
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Alternating series test Examples
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SOLVED: Theorem 2.7.7 (Alternating Series Test). Let (an) be a sequence satisfying a1 >= a2 >= a3 >= ... >= 0. Then, the alternating series Σ((-1)^n * an) converges.Proof: The conditions of this theorem are outlined in Exercise 2.7.1. One consequence of these conditions is that an >= 0 for all n. Several proofs of Definition 2.7.8 - Convergence of a Series are given in Exercise 2.7.1.Exercises Exercise 2.7.1. Proving the Alternating Series Test (Theorem 2.7.7) amounts to showing that the sequen
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