Question #8ed5a Calculus Power Series Determining the Radius and Interval of Convergence for a Power Series 1 Answer Cesareo R. May 30, 2016 #(df)/(dx)(x) = sum_{i=1}^n (n-i)a^i x^{n-i-1}# Explanation: #f(x) = sum_{i=0}^n a^i x^{n-i}# so deriving #(df)/(dx)(x) = sum_{i=1}^n (n-i)a^i x^{n-i-1}# Answer link Related questions How do you find the radius of convergence of a power series? How do you find the radius of convergence of the binomial power series? What is the radius of convergence for a power series? What is interval of convergence for a Power Series? How do you find the interval of convergence for a power series? How do you find the radius of convergence of #sum_(n=0)^oox^n# ? What is the radius of convergence of the series #sum_(n=0)^oo(x-4)^(2n)/3^n#? How do you find the interval of convergence for a geometric series? What is the interval of convergence of the series #sum_(n=0)^oo((-3)^n*x^n)/sqrt(n+1)#? What is the radius of convergence of the series #sum_(n=0)^oo(n*(x+2)^n)/3^(n+1)#? See all questions in Determining the Radius and Interval of Convergence for a Power Series Impact of this question 1350 views around the world You can reuse this answer Creative Commons License