find the radius and the interval of convergence of x32nnnSol

Solution

given series is convergent if

lim n---> infinity (x-3)^2n/n^n=0

now

(x-3)^2n/n^n=((x-3)^2/n)^n

now this limit is equal to 0

for any value of x

hence

interval of convergence is

(-infinity,infinity)

and radius of convergence is infinity