PPT-Sect. 9-6 Alternating Series

Alternating Series A series whose terms are alternately positive and negative If n starts at 1 then the first term is negative If n starts at 1 then the first term is positive Alternating Series Test . This is accomplished through a sequence of s trategic replacements of rectangles with others of lesserarea Inthelimitweobtaintheregionbeneath thecurve and above the axis between thevalues of one and two Math Mag 83 2010 294 doi 104169002557010X52183 1. For the series
n
1  1  n1 n 3
(a) Does the series converge absolutely, converge conditionally, or diverge? Support your answer.
(b) If the series converges, use partial sums to find th Testing Convergence. at Endpoints. Alternating Series. A series in which the terms are alternatingly positive and. n. egative is an . alternating series. .. Examples:. This is a geometric series with . DEFINITION. Absolute . Convergence. Verify that the series. converges absolutely.. This series converges absolutely because the positive series . (. with . absolute values. ) is a . p. -series with . 9-D . Comparison Tests . The Direct comparison Test . If 0 < a. n . < . b. n. . . for all n and positive terms, then:. If the larger series converges, then the smaller series must also converge. . Sum of a Geometric Series. Let . c. 0. . If |. r. | < 1, then. If |. r. | ≥ 1, then the geometric series diverges.. Sum of an Infinite Geometric Series (80). Sum of an Infinite Geometric Series (80). 4Thepresentversionisasimplicationofapreviousimplementation,describedinanunpublisheddraft(AltenkirchandOury2008). (Sects.2.2and2.3),equality(Sect.2.4),familiesofdatatypes(Sect.2.5),andnallyinduction- Learning Outcomes. Distinguish between alternating and direct current.. State . the frequency of UK mains electricity.. Describe . how the potential of the live wires varies each cycle.. State . that the potential of the neutral wire is approximately . Acts 28:16-22. The Meaning of “Sect”. A “sect” is a “section” separated from others. . “Sect” is translated from a Greek word that is also translated . heresy. or . faction. .. It is a work of the flesh (Galatians 5:20). Calc. BC. Objectives. Use the Alternating Series Test to determine whether an infinite series converges.. Use the Alternating Series Remainder to approximate the sum of an alternating series.. The simplest series that contain both positive and negative terms is an . Occasionally, a series may have both positive and negative terms and not be an alternating series. For instance, the series. has both positive and negative terms, yet it is not an alternating series. One way to obtain some information about the convergence of this series is to investigate the convergence of the series. K.Gauravetal.:MorphologyoftheKosimegafanchannels323 Figure1.TheKosimegafan(KMF)boundaryshownonLandsat8satelliteimage(acquiredon11November2013).Redandbluepointsontheimageshowthelocationsofcross-section What is the need for an AC circuit?. The generation of single phase voltage.. The relation between time and angle.. The maximum, average and effective value.. The form factor and peak factor.. Phasor representation of sinusoidal waveform.. AC. )?. Why the AC generated? What is the need for an AC circuit?. Alternating Current Waveforms. Different (Alternating) Sinusoidal Current Waveform Generators. There are 2 types of Current. DC = Direct Current .