Assume we have the following series:

    s1=0.1 + 0.397953 t + 0.592849 t^2 + 0.588719 t^3 + 0.438295 t^4 + 
       0.260863 t^5 + 0.129195 t^6

    s2=0.000027 t + 0.0000172737 t^2 - 8.40515*10^-6 t^3 + 
       6.14728*10^-6 t^4 - 2.83586*10^-6 t^5 + 1.1533*10^-6 t^6

Can I evaluate the radius of convergence for both of them? in Mathematica?

In general how can evaluate the radius of convergence is |an/an+1| for large n for any series in mathematica?