1. The problem statement, all variables and given/known data Σ(n=0 to ∞) ((20)(-1)^n(x^(3n))/8^(n+1) 2. Relevant equations Ratio test for Power Series: ρ=lim(n->∞) a_(n+1)/a_n 3. The attempt at a solution I tried the ratio test for Power Series and it went like this: ρ=lim(n->∞) (|x|^(3n+1)*8^(n+1))/(|x|^(3n)*8^(n+2)) =20|x|/8 lim(n->∞) 1 =20|x|/8 20|x|/8<1 |x|<2/5 So radius of convergence=2/5. However when I input the power series into Mathematica, it says that the radius of convergence should be 2 (http://goo.gl/9nAHoS) Where am I going wrong in my calculation?