What is the power series for #ln(1+x^4)#? Calculus Power Series Introduction to Power Series 1 Answer A. S. Adikesavan · Alexander Jul 2, 2016 #x^4-x^8/2+x^12/3-...+(-1)^nx^(4n)/n+...#. for # --1 <= x <= 1 # Explanation: Use #ln(!+X)=X-X^2/2+X^3/3-...+(-1)^nX^n/n+...#, #-1 < x <=1 # Here, #X=x^4 and -1 < x^4 <= 1 to -1<= x <=1# Answer link Related questions What is a Power Series? How do you find the power series for a function centered at #c# ? How do you test a power series for convergence? How do you find the radius of convergence for a power series? How do you find the interval of convergence for a power series? How do you find a power series representation for #f(x)=1/(1+x)^3#? How do you find a power series representation for # x^2 / ( 1 - 2x )^2#? How do you find a power series representation for # (1+x)/((1-x)^2)#? How do you find a power series representation for #(x-2)^n/(n^2) # and what is the radius of... How do you find a power series representation for #f(x)=3/((1-5x)^2)# and what is the radius of... See all questions in Introduction to Power Series Impact of this question 10364 views around the world You can reuse this answer Creative Commons License