原式=lim(n->∞){4[(1+(1+2^n+3^n)/4^n)^(4^n/(1+2^n+3^n))]^[(1/n)(1+2^n+3^n)/4^n]}
=4e^{lim(n->∞)[(1/n)(1+2^n+3^n)/4^n]} (应用重要极限lim(z->0)[(1+z)^(1/z)]=e)
=4e^{lim(n->∞)[(1/n)((1/4)^n+(2/4)^n+(3/4)^n)]}
=4e^[0*(0+0+0)]
=4.