What is the interval of convergence of #sum {(x-7)^n}/{(n!)7^n} #? Calculus Power Series Determining the Radius and Interval of Convergence for a Power Series 1 Answer Cesareo R. Jul 9, 2016 Converges for all #x in RR# Explanation: #sum {(x-7)^n}/{(n!)7^n} = sum_{n=1}^oo((x-7)/7)^n/(n!) = e^{((x-7)/7)}# 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 2012 views around the world You can reuse this answer Creative Commons License