How do you find the power series representation for the function #f(x)=(1+x)/(1-x)# ? Calculus Power Series Power Series Representations of Functions 1 Answer Wataru Sep 9, 2014 Recall: #1/{1-x}=sum_{n=0}^infty x^n=1+sum_{n=1}^infty x^n# By multiplying by #x#, #x/{1-x}=sum_{n=0}^infty x^{n+1}=sum_{n=1}^infty x^n# So, #{1+x}/{1-x}=1/{1-x}+x/{1-x}=1+sum_{n=1}^infty x^n+sum_{n=1}^infty x^n# #=1+2sum_{n=1}^infty x^n# Answer link Related questions How do you find the power series representation for the function #f(x)=ln(5-x)# ? How do you find the power series representation of a function? How do you find the power series representation for the function #f(x)=sin(x^2)# ? How do you find the power series representation for the function #f(x)=cos(2x)# ? How do you find the power series representation for the function #f(x)=e^(x^2)# ? How do you find the power series representation for the function #f(x)=tan^(-1)(x)# ? How do you find the power series representation for the function #f(x)=1/(1-x)# ? How do you find the power series representation for the function #f(x)=1/((1+x)^2)# ? How to find the Laurent series about #z=0# and therefore the residue at #z=0# of #f(z) = 1/(z^4... Question #87417 See all questions in Power Series Representations of Functions Impact of this question 5988 views around the world You can reuse this answer Creative Commons License