MAT146-TestsforConvergence(FinalExam) ar^(n-1),cgtif|r|<1-ANS-Whatisageometricseries?Whenisitconvergent?a/(1-r)-ANS-Whatisthesumofageometricseries?G.S.,integraltest,definitionofcgt/dgtseries-ANS-What3testscanyouusetofindthesumof aseries?1/n,alwaysdgt-ANS-Whatisaharmonicseries?Isitcgtordgt?lim(asnapproachesinfinity)ofan -DNE=dgt -existsanddoesn'tequal0=dgt -inconclusiveif=0-ANS-Whatisthetestfordivergence(TFD)?lim(asnapproachesinfinity)ofSn -exists=cgt -DNE=dgt Snissumofseries(writeoutallterms)-ANS-Howdoyoudetermineconvergencewith definitionofcgt/dgtseries?Canonlyuseiff(n)iscontinuous,positive,decreasingon[1,infinity) then,cgtifintegral(from1toinfinity)iscgt dgt,ifintegral(from1toinfinity)isdgt-ANS-Howdoyoudetermineconvergencewiththe integraltest?-geometricseries -harmonicseries -definitionofcgt/dgtseries -TFD(testfordivergence) -integraltest -comparisontest -limitcomparisontest -ratiotest -roottest -p-seriestest -p-alternatingseriestest -Alternatingseriestest-ANS-Namethe12tests buildyourownseries -ifbiggercgt,thensmallercgt
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