对任意ε>0;n>1时Abs((√n+1)/(3√n-1)-1/3)=2/3*Abs(1/(3√n-1)) =2/3/(3√n-1) <2/9*(1/√n)<(1/√n)取N=1/ε^2;则当n>N时,Abs((√n+1)/(3√n-1)-1/3)<ε;证明完毕