Find the radius of convergence of the following series. Does it converge or diverge? #sum_(n=1)^oo((-1)^nx^n)/root(9)(n)#
#sum_(n=1)^oo((-1)^nx^n)/root(9)(n)#
1 Answer
Apr 3, 2018
By the ratio test:
#R = lim_(n -> oo) (((-1)^(n + 1)x^(n + 1))/(root(9)(n + 1)))/(((-1)^nx^n)/(root(9)(n))#
#R = lim_(n ->oo) |(-x)| root(9)(n)/root(9)(n + 1)#
The limit in
Thus
#|x| < 1#
The radius of convergence is
Hopefully this helps!
