Alternating Series Section 8 5 AP Calc Alternating

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Alternating Series Section 8. 5 AP Calc

Alternating Series Section 8. 5 AP Calc

Alternating series- terms alternate signs

Alternating series- terms alternate signs

Thm 8. 14 Alternating Series Test Let an>0. The alternating series and converge if

Thm 8. 14 Alternating Series Test Let an>0. The alternating series and converge if the following two conditions are met. 1) 2)

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

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

Thm 8. 15 Alternating Series Remainder If a convergent alternating series satisfies the condition

Thm 8. 15 Alternating Series Remainder If a convergent alternating series satisfies the condition the absolute value of the remainder RN involved in approximating the sum S by SN is less than (or equal to) the first neglected term. That is,

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

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

Determine the number of terms required to approximate the sum of the series with an error less than 0. 001. (Then approximate the value of the series with your answer. )

Thm 8. 16 Absolute Convergence If the series converges, then the series also converges.

Thm 8. 16 Absolute Convergence If the series converges, then the series also converges.

Alternating Harmonic: Test convergence with the Alternating Series Test

Alternating Harmonic: Test convergence with the Alternating Series Test

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

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. A) B)

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

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

Finite Series: can be rearranged without changing the value of the sum. Not necessarily

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

Look at:

Look at:

Section 8 6 Alternating Series An Alternating SeriesSection 8 6 Alternating Series An Alternating Series
11 5 Alternating series An alternating series has11 5 Alternating series An alternating series has
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ALTERNATING SERIES series with positive terms series withALTERNATING SERIES series with positive terms series with
ALTERNATING SERIES series with positive terms series withALTERNATING SERIES series with positive terms series with
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Section 9 6 Infinite Series Alternating Series AbsoluteSection 9 6 Infinite Series Alternating Series Absolute
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Alternating Currents An alternating current such as thatAlternating Currents An alternating current such as that