What is the interval of convergence of sum_1^oo (3n)/n^(x)? Calculus Power Series Determining the Radius and Interval of Convergence for a Power Series 1 Answer Cesareo R. Aug 4, 2016 x>2 Explanation: For x-1>0 which is the condition for which k^{-(x-1)} decreases monotonically, we have sum_1^n 3 k^{-(x-1)} le int_1^n 3k^{-(x-1)}dk +3= n^{2-x}/(2-x)-1/(2-x)+3 and also for 2-x < 0 we have lim_{n->oo}n^{2-x}/(2-x)-1/(2-x)+3 = 1/(x-2)+3. So we have sum_1^n 3 k^{-(x-1)} le 3/(x-2)+3 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 1497 views around the world You can reuse this answer Creative Commons License