ch11s5

# ch11s5 - 11.5 Alternating Series An alternating series is a...

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11.5 Alternating Series An alternating series is a series whose terms are alternately positive and negative. They will often have the term (-1) n as part of the definition of the series. The test for determining convergence or divergence as follows: The Alternating Series Test If the alternating series () 1 1234 1 n n bbbbb b =−+−+ > L 0 n satisfies for all n and then the series is convergent. 1 nn ab b + ()l im 0 n n bb →∞ = Example: Determine convergence or divergence for each series. 2 1 2 11 (1 ) l n ) ) 1 3 n n n c n n ∞∞ == = −− + + ∑∑ ∑ 1 n n b Look at Example 1 on page 728. This series is the alternating harmonic series and it is convergent. Estimating Sums We have a theorem to use when estimating the sum of a convergent alternating series. Theorem: If is the sum of an alternating series that satisfies

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ch11s5 - 11.5 Alternating Series An alternating series is a...

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