Download presentation

Presentation is loading. Please wait.

Published byLexus Crompton Modified over 2 years ago

1
Section 11.5 – Testing for Convergence at Endpoints

2
Common Series to be used…. Harmonic Series - DIVERGES p-Series Converges if p > 1 Diverges if p < 1 Comparison Test for ConvergenceComparison Test for Divergence

3
acts like converges by the comparison test to the p-series with p = 2. Makes terms smaller

4
diverges by the nth term test for divergence. acts like diverges by the comparison test to the p-series with p = 1.

5
ABSOLUTE CONVERGENCE

8
Alternating Series Test converges if both of the following conditions are satisfied: If a series converges but the series of absolute values diverges, We say the series converges conditionally. CONDITIONAL CONVERGENCE – (AST)

9
Determine whether the series is converges conditionally, converges absolutely, or diverges. The series converges conditionally

10
Determine whether the series is converges conditionally, converges absolutely, or diverges. Determine whether the series is converges conditionally, converges absolutely, or diverges. The series diverges by the nth term test for divergence

13
Find the interval of convergence for If x = -1, converges, alternating series test If x = 1, diverges, harmonic series Interval of convergence [-1, 1) ? ?

14
Find the interval of convergence for If x = -7, diverges, nth term test If x = 1, diverges, nth term test Interval of convergence (-7, 1) ? ?

15
Find the interval of convergence for Interval of convergence

16
Find the interval of convergence for If x = 2,diverges, harmonic series If x = 4, converges, alternating series test Interval of convergence (2, 4] ??

17
Find an upper bound for the error if the sum of the first four terms is used as an approximation to the sum of the series.

18
Find the smallest value of n for which the nth partial sum approximates the sum of the series within 0.005.

Similar presentations

OK

9.5 Alternating Series. An alternating series is a series whose terms are alternately positive and negative. It has the following forms Example: Alternating.

9.5 Alternating Series. An alternating series is a series whose terms are alternately positive and negative. It has the following forms Example: Alternating.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on history of australia's government Ppt on javascript events textbox Ppt on principles of object-oriented programming languages Ppt on series and parallel combination of resistors in series Ppt on photovoltaic power generation system Ppt on earth movements and major landforms in spain Ppt on social networking dangers Ppt on network topologies Ppt on metallic and nonmetallic minerals Ppt on appropriate climate responsive technologies for inclusive growth and sustainable development