Question

It N 3 points Which of the following statements is FALSE? There exists a power series with interval of convergence (-0,0). o A power series of a function and its derivative have the same radius of convergence. A power series of a function and its integral have the same radius of convergence. There exists a power series with interval of convergence (0,0).

Answer 1

but considere hao hl xh) anta n! (n+1)! now Ratio tor Los lim | antl if Lal Serps convergne haze * = ml xht hy (141) xx (x) at lim ngut (RAIDA 2 *L=und M htl u 4. 기이 is a L =0 21 hence given series is convergent absolutely ° ¢ Inferral of convergenne convorgene (186) hen there exista power Serjes Rachus | R=0 it consider xn had x? M 8 E no a DX ox nao ona hx ht1-) Ontl = (+1) x Rabio test * L- Antl)x" um havo Cim letto) * thl hau 27 * (to x <1 مرا Io a-klas Radius of convergene 1-(-1) a loca (11) a(R=))

Power Series & its integral also have same radius of conrem ?W ६ xht nl An antia x²+2 7+2. La XH2 that Allt * من با y lim ny M(143) th 7. (i+bo) (4+5) kit -kxal H-1) & Ioca (1.1) & Radaus of convergence &= G 2 co now Consider { xh only no antl=x +) ana th I= 4m they h-SO x" & lxk) -K XK ñ 10 E = (1,1) R = O !-(-1) " There exist power series with loc with IoC (-2,0) & A Power series of a function of its derivative have forme Radius of Convergene hone falfe Statement There Exiets a Power gerjes with Interval of convergene Condor pane Corso Solat lost option