DCT Tutorial Materials - Edubirdie

University:
California State University, Northridge
Course:
MATH 150B | Calculus II
Academic year:

2023
Views:

176

Pages:

6
Author:

Alifah C.

10.4Wednesday March 24,2021 11:28 AMCanv??anDiv.DCTdn 6I larg ndnyo(n)oExp Check for Conv./DivDanEanE3+ sin\1an>0n2aconvn=1dixD3+ (singL<vn for large n4ntvnysuConvyourn=1andivXIn)TE3NY or 1/2ntvnhasntn ntvHdiv - pseries x p=1Series3n > 2n ' > ntvnor div Halmmanic3n >n+vn1/1DCTnby>ntun^3 OUL yiuntunHence, Enivn 3 div by DC'3E3ntvn8ICTE??anFind bn s.tn=1E bn islimitan>o, bn>oKnownIliman =c>othen both (Ean and Ebn) arebn8finiteConv. or both div.lim an = 0 and Ebn conv then Ean Conv.bnn-r2lim an = 00 and Em div then Can div.hnn8ExpcheckforCom/DivLCT00anfind bn =1/51/5divD-46I E fan 1/2H.Sevidn=1n=ltan thsindcostan = lim= limlimhnn-soo1/1n-soo1/hes' 8and n-\us t has= lim sind lim Cos 1/2u=11/5nswn-soo= lim sinu islim cosuunsot= (1) coso =(v(1)=1704-90Hence, E ten 1/2 div by LCT30,8nFindbr=s.tann22En+2n2Sconv. p-seriesn= \nx2(im an = lim xr= lin n+28/8bnn-s an-so 2n-90014n2 (Inz)= him 1+2Inz= lin170318n-w2 (Inz)n-1002 In2A+B+ntz"Hence,EConu by LCTconv.n?n2w00nE+=12)n2n+22n 2"nnh='n=1Cconv.n-aeomF CconvConv. P.SorLHence,EntityConv. by DCTgeomseriesn'12comLCT,83anEn + 2Find bn=n20+n2+5n=\Econv.cn+2lim an limn3+n2+5= lim(n+2)n = 1>0n3+n2+5nownow bn nso/1'En+2Hence,conv. by LCTCIDFind bn=nts.tton+1ann'+2n=1EEknowndiv-psersapplyinit'sn+1n'+2Cananlim= limSAT Vnbn=\Inswnewnawcont.limn'+n=limn'tn = ST=1>0n-sayn'++n-so n'+2Hence, Cn+'div byLCT Hence,E.n+'div byLLn'++00n+1Use LCT and = DCT22rishn=1an\n=LCT:Find bn=2.51.5hit{Conv.p-serisn+1him Thn an = limCFlim n+1 = \ >0nson8n-s 00 n'nEn+1n'tnconv. by LCTDCT8conv.n+1ntnTh{2A = 2

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