Given number: n!n2 It is a series of species an(cx−x0)dn - power series. The radius of convergence of a power series can be calculated by the formula: Rd=cx0+limn→∞an+1an In this case an=n!n2 and x0=0 , d=0 , c=1 then 1=n→∞lim(n+1)2n2n!(n+1)! Let's take the limit we find