Alternating Series Section 8.5 AP Calc

Alternating series- terms alternate signs

Thm 8.14 Alternating Series Test Let a n >0. The alternating series and converge if the following two conditions are met. 1) 2)

Determine the convergence/divergence of the series: A)B) C)

Thm 8.15 Alternating Series Remainder If a convergent alternating series satisfies the condition then the absolute value of the remainder R N involved in approximating the sum S by S N is less than (or equal to) the first neglected term. That is,

Approximate the sum of the series by using the first 6 terms

Determine the number of terms required to approximate the sum of the series with an error less than (Then approximate the value of the series with your answer.)

Thm 8.16 Absolute Convergence If the series converges, then the seriesalso converges.

Alternating Harmonic: Test convergence with the Alternating Series Test

Definition of Absolute and Conditional Convergence 1) is absolutely convergent if converges. 2) is conditionally convergent if converges but diverges.

Determine convergence/divergence- classify convergence as absolute or conditional. A)B)

Determine convergence/divergence- classify convergence as absolute or conditional. C)

Finite Series: can be rearranged without changing the value of the sum. Not necessarily true with Infinite Series. Absolutely convergent: rearranged get same sum Conditionally convergent: may get different sum

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