Given number: ne−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=ne−n2 and x0=0 , d=0 , c=1 then 1=n→∞lim(n+1ne−n2e(n+1)2) Let's take the limit we find