Question

answer 1 and 2 please

1) When is the basic comparison test useful? (What kinds of series woul d you use it for?) 2) How do the tests you've already encountered assist in use of the com parison tests?

Answer 1

80/? Comparision test 10 ID nabo Vn rest I. f I up and 5 Vn are series of positive terms and Evn 18 such that Uns KVM eigent and these 18 abositive Constant k Vn , then sun is also convergent Test II- f EUn and Evy are series of positive terms and Evni8 const k such that abositive contrk kg. . de vergent and there is Vn, Then EUR is also divergent , Test II. J E Un and EVA are series of positive terms and Evgi 8 | Convergent and there is apositive constant k such that uns kVtnym Then Eun is also Convergent Test N- If EUn and Evy are two seises of boxitive terms and Evnis diverses and there is positive constant k such that Ug> kvm Vn sm then Eug is also divergent | Testy Y EU, and Evn are two positive term series and there exist two | positive Canett H and K (ande pendent of n) and a series positive integer m such that HK un sk #nym Test VI - Let E Un and Even be two positive team Beries cu 4 lim un at Sfinite and nonzero then EUn and EK both Converge or diverge to be ther. :0 and En Convergeh Then Eun also converges f) din Un and Even diverges, then Evin also divenges he generally apply Test VI Ċ only and that is why Test Dio is usually | Catted in comparison test. It is very useful and will be very frequently applied Hence, it8 Statement should be carefully mastered. Teste det EUn and Evy be two form positive term Series og un y un tnym and Evn is convergent, then Eun is also convergent. Po Unt). Vints O y una Un tnym and E von 18 divergent, then E Um is also divergent Unti Vent f1218t of all we check Asies 18 positive terms series, then we check any test appied ng any test applied then we use Comparision test i Exossint Un= sint , sinto 3 ħ Than By P test et divergent 80 " Esint diverses @ E ten unhentis vin e Mos un = I bo By Pitest E the convergent 80 Enchan convergent 15 on comparision test mostly prest e bip test are encountered assist and they are always cheful Ptest IB Most Impostant for Combonision test we are gave above two examples in which we used P-fest abreddy. prest Ebe converges if p>I and diverses if Pst problems on componision when you do most test. Its better toay to under standing this test & must learn all test which are used in com ih are used in companijonte