Find the radius of convergence of the power series: $\displaystyle ((n!)^2/(2n)!)x^n$

My answer; 0 using $\displaystyle a(n+1)/a(n)$

Find the limits, if they exists, of

i) $\displaystyle 100(ln(x))/x^3$ as n tends to infinity

ii) $\displaystyle (sinx-x)/(cosx -x^2-1)$ as n tends to 0

My working i) pretty certain its infinity but not sure how to show it

ii) no idea on this one.