Menu Close

Given-that-1-lt-x-lt-1-find-the-expansion-of-3-2x-1-x-4-x-2-in-ascending-power-of-x-up-to-and-including-the-term-in-x-3-




Question Number 161823 by MathsFan last updated on 22/Dec/21
 Given that −1<x<1, find the   expansion of  ((3−2x)/((1+x)(4+x^2 ))) in   ascending power of x, up to and   including the term in x^3
Giventhat1<x<1,findtheexpansionof32x(1+x)(4+x2)inascendingpowerofx,uptoandincludingtheterminx3
Answered by mr W last updated on 23/Dec/21
=((3(1−((2x)/3)))/(4(1+x)(1+(x^2 /4))))  =(3/4)(1−((2x)/3))(1−x+x^2 −x^3 +x^4 −...)(1−(x^2 /4)+(x^4 /(16))−...)  =(3/4)[1+(−(2/3)−1)x+(1−(1/4)+(2/3))x^2 +(−1−(2/3)+(2/(3×4))+(1/4))x^3 +...]  =(3/4)[1−(5/3)x+((17)/(12))x^2 −(5/4)x^3 +...]  =(3/4)−(5/4)x+((17)/(16))x^2 −((15)/(16))x^3 +...
=3(12x3)4(1+x)(1+x24)=34(12x3)(1x+x2x3+x4)(1x24+x416)=34[1+(231)x+(114+23)x2+(123+23×4+14)x3+]=34[153x+1712x254x3+]=3454x+1716x21516x3+
Commented by peter frank last updated on 23/Dec/21
thank you
thankyou

Leave a Reply

Your email address will not be published. Required fields are marked *