Question

Š ak Suppose k k+1 (a) Find the radius and interval of convergence of the above power series (b) Find the power series for f' (2). (c) Find the power series for S* f (x) dx' (d) Find $(3) (0) (e) Find the first three nonzero terms of the power series for (ſ (2)) ?

Answer 1

O fox) = { K L k xk k=1 (a) Jak E k ok kt K kt xk - et akt et (KH xkl. kH et (k+1)² pxl KCK+2) Kto kt2 kx' ka ta 1x1 for Convergence, 1 - 1x121 Radius of convergence, Ral & 1x1</ Intequal of Convergence, & EX-1, 1) alkas I K f(x) = NO K xk kt k=1 Dn.s to a f'(x) ad ETH da k=1 K² x f'(x) kal E k dex" ktlax IME (KH) DO K-1 WI I (KH) 10 k (Q"T!) K dx = dx = Sca **) ** { fons de ut KHI KH kt Ю x k 2 k=1 I AM (O) Xt KEO (k (d) F%) = 3 (3+1 le 313 4 To 3x6 = f = 30 4

원 KH yix) = J x + + + 1 - (fr) = ( -- ( 44 - - ) + 즐용들아 들자 좆 비 에어 1 odlry 2 + 3x3 모 - 일 000 1 2 t (fr): 쪽아주름 에 1g - 사이 of love is first Three non zero Person of fox)?