Question

(1 point) Find a power series centered at a = 0 for the function ln(1 + x) When you have found the series, enter the sum of the first five non-zero terms of the series. Find the radius of convergence R of the power series. R= 1 Use the power series you found above, to build a power series for the function f(x) = x? ln(1 + x). Again, enter the first five non-zero terms. What is the radius of convergence R of this power series? R=

Answer 1

# we know that no ni +1 2n(1+2) = È un pat +C at x=0 we get cao enc142) = **-* +39 - + 4 + - first foue nem zeno terms = 2- + -**+21 R= lim | +2 = 1 nuten +1 nro First five non zero terms + x3 lnc 144) = 33 3 60" = 4:" = 49-* - * * Ra lim mt?)= ! # (-)" xn o itsx = 647" (33" - 643" 3" x) nao - 1- 32 +972-2723+ 8179 feruirth partial bum

we know that no 2n ifq2 = 40"x2n t 5 ngenti dx te - ant! não Iltare a S Sat x=0,20 tom-(x)= ? 2h+ 2nti ! Turcos não anti . tant (24) = 8 (on genta neo 2171 S team (40) dx = .COM SIT ANG wh x8n45 tamt (89)dx = Aą (8h+5) (2n+1) res to zero at aco) it five terms = 221 - 213 - 229 39 1 105 203 let 333