5E TLW identify a series and apply them. Series- addition of the terms of a sequence The corresponding series of 𝑢 𝑛 is 𝑢 1 + 𝑢 2 + 𝑢 3 + . . . The sum of a series: 𝑆 𝑛 = 𝑎 1+ 𝑎 2 + 𝑎 3+…+ 𝑎 𝑛 21, 23, 25, 27, . . . ,49 is a...
INFINITESEQUENCESANDSERIES 10.1SEQUENCES Asequencecanbethoughtofasalistofnumberswritteninadefiniteorder:a1,a2,a3,…,an,…Thenumbera1iscalledthefirstterm,a2isthesecondterm,andingeneralanisthen-thterm.Wewilldealexclusivelywithinfinitesequencesandsoeachtermwillhaveasuccessoran+1.NOTATIONThesequence{a1,a2,a3...
高等数学英文版课件PPT 09 INFINITE SEQUENCES AND SERIES精选.ppt,Again we put x=a in Equation 3. The result is f (a)=2c2 By now you can see the pattern. If we continue to differentiate and substitute x=a, we obtain f (n)(a)=2·3·4·…·ncn=n!cn Solving t
INFINITESEQUENCESANDSERIESChapter910.1SEQUENCESAsequencecanbethoughtofasalistofnumberswritteninadefiniteorder:a1,a2,a3,…,an,…Thenumbera1iscalledthefirstterm,a2isthesecondterm,andingeneralanisthen-thterm.Wewilldealexclusivelywithinfinitesequencesandsoeachtermwillhaveasuccessoran+1.NOTATIONThesequence{a1,a2...
12.3 – Geometric Sequences and Series Arithmetic Series Sum of Terms Geometric Series Sum of Terms Arithmetic Sequences Geometric Sequences ADD To get next term MULTIPLY To get next term Vocabulary of Sequences (Universal) Find the next three terms of 2, 3, 9/2, ___, ___, ___ 3 –...
e.g.1Givethe1sttermandwritedowna recurrencerelationforthesequence 1,4,16,64,...Solution:1stterm:Recurremcerelation:u11un14un Otherlettersmaybeusedinsteadofuandn,sotheformulacould,forexample,begivenas ak14ak SequencesandSeriesRecurrenceRelationse.g.2Writedownthe...
Chapter3SequencesandSeries(PartB)Topics GeometricProgressionTheBinomialExpansion 2 GeometricProgression Ingeneral,ageometricprogressioncanbewrittenas:(n−1)a,ar,ar,KK,ar 2 ,KK wherea=thefirsttermr=thecommonratio 3 GeometricProgression Thenthterm,un=ar(n−1)Thesumofthefirstnterms,a(rn−1)Sn=...
Arithmetic Sequences and Series Thinking Evaluate1+3+5+7+…+99.2500 ArithmeticSequencesand Series Anintroduction………1,4,7,10,139,1,7,156.2,6.6,7,7.4,3,6 351227.239 ADDTogetnextterm ArithmeticSequence:Asequenceinwhichthereisacommondifferencebetweenconsecutiveterms.3,5,7,9,11,13,...Th...
级数数列sequencesseriessequenceterm Sequences & Series Sequence: A function whose domain is a set of consecutive integers. The domain gives the relative position of each term of the sequence: 1 st , 2 nd , 3 rd , and so on. The range gives the terms of the sequence. Finite Sequence: ...
Geometric Sequences and Series 9.3GeometricSequencesandSeries Objective •Tofindspecifiedtermsandthecommonratioinageometricsequence.•Tofindthepartialsumofageometricseries GeometricSequences •Consecutivetermsofageometricsequencehaveacommonratio.DefinitionofaGeometricSequence •Asequenceisgeometriciftheratiosof...