Question

12 Follow the steps below to find a power series representation for f(x) = - 2? + 40-50 12 22 + 40 -5 А 2-1 + В +5 , where A = and B = Find the first 4 non-zero terms in the power series representation of the following fractions: t... 2 - 1 2 +5 Therefore f(a) = 12 2 + 40-5 - =co +212 + c22a +..., where

Answer 1

Hope it helps.All the best

QSCI) Given: - frx)= 12 =) frx)= 12 . (x-1)(x+5) 0 2 Uxus 12 12- ACX+5)+B(x-1) 12. - = A + B x-1)(x+5) Xos X+5 put x=b in ew @ we get put *:-s in ex@ we get 12 = AC1+5) =) A = 12 => A=12 =2 =) (8=23 12+ 86-5-1) => B=-12 => B=- 11 (x-1)(x+5) X-1 *+5 ( x-1 X+5 (X-1 SIJI We know that the power series of (1-x5': S+x+x+x3+ ---.. and (1+x)"; 1-x+x2-x3-.... == = -(1-x34= -(1+x+*+x2)+--- = ---x-x?**. - +/X xin m.is | - 5 25 125 6 (schn] =***** a -1-1 X X X+ -6+ x X-1 +1 1+ x21 -X + X 5 -xix2 *****:} . 5 +x°[++tes] -24 Xal olu 5 +X 25 125 625 now L-484.25 1248X If - - , x-1 25 125 15.] >> FONDE 2 - Les 2933* 2.... - compare ea® (with foxsa.co+ Cox+Cqx?+Cgx?t... . C - -252 125 625