i need to compute lim (a^n-b^n)^(1/n) when a>b>0. lim ((3n)!/((2^3n)n!(2n!)))^(1/n) where i need to use the lemma that: if an>0 for every n, and lim(x_n+1/x_n)=L then lim x_n^(1/n)=L, how to use it here? for the first i used practically everything i know, the formual for a^n-b^n, and the fact that 0<a^n-b^n<a^n and lots more algebraic techniques, apparently not everything. your help is appreciated.