How do you find the taylor series expansion of #f(x) =x/(1+x)# around x=0? Calculus Power Series Constructing a Taylor Series 1 Answer vince May 29, 2015 You know that #1/(1-x) = 1 +x + x^2 + x^3 + ...# so, #1/(1+x) = 1 - x + x^2 - x^3 + ....# therefore, #x/(1+x) = x - x^2 + x^3 - x^4 + ... = sum_{k=0}^\infty (-1)^(k)x^(k+1)# Answer link Related questions How do you find the Taylor series of #f(x)=1/x# ? How do you find the Taylor series of #f(x)=cos(x)# ? How do you find the Taylor series of #f(x)=e^x# ? How do you find the Taylor series of #f(x)=ln(x)# ? How do you find the Taylor series of #f(x)=sin(x)# ? How do you use a Taylor series to find the derivative of a function? How do you use a Taylor series to prove Euler's formula? How do you use a Taylor series to solve differential equations? What is the Taylor series of #f(x)=arctan(x)#? What is the linear approximation of #g(x)=sqrt(1+x)^(1/5)# at a =0? See all questions in Constructing a Taylor Series Impact of this question 2109 views around the world You can reuse this answer Creative Commons License