Question

3.- Find the interval and radius of convergence of the following power series. 6'2" (a) (-1)" (x - 2)" (b) m3n 4.- Find the points of intersection of the pairs of curves. n=1 nel (a) r= 2 cose, r=1+cos (b) p2 = cos(26), r2 = sin (20)

Answer 1

N . Unti (3) (a) soln since the green the given Hin 6n sin Now, u - L4 (-10 คน (ก41) n! Hint & Hence sudius of convergence ii of TRES intestealcf converses alo.f) re IR zetate (by Rakibat Nole Ratio best gt Lt un = 131 - cat nto dc1- div (fxposities ІІ - НА » Fayьс се (6) since, the given S (81-290 n.3n ( 1 (sath Alleta) stig nyt nt | D.30 (0-2) Gw 1977-21 n n+i). 3nft no n.3n 15-2) nel - 312-21 = 10-2/13 ISOR=3 2-3 ene 2+3 = 42025 NOW - 4 est by celtes is meeting Sining 965-1, then tuin 5 601-1-2)" - {HITE htm n-31 5z

가 Ifn-5 then series becomes s 19-21 swa 377 n.zn o Wa n.3n n divergent by Auxilarly series Hence intence of onvergence in J= (-5) Auxilarly series E the if prices Pel div. (4 (6) since 8= 21050 1+ loso from and 121, we get 2 caso = litloso 2,0) where -) 1080 = 1 =) 1030 = Los Da, nz 0, 1, 2, or caso = (as 2 0 = 2n12 O= annta, de 6 O=0, 20 au Gel Hare pointy intersection is i etalo,ole (2,0) 0=0, 20, 1911, 617-- So equction (had @ Cats or intersect cat o = 2n1, ntz 5 8 2 (asso - art 82- Sin/20) = 1082 O = Sinzo = tanzo = 1 =1 ten20-stent 20= /y = 0 ten 20-taly S 20 = 2 0-13 (nrad) on-0,072 0-1451