證明:(n->無窮)limn^(1/n)=1用加逼準則證明下

證明:(n->無窮)limn^(1/n)=1用加逼準則證明下

令a_n = n^(1/n)-1>=0
那麼n>1時n =(1+a_n)^n = 1+n*a_n+n(n-1)/2*a_n^2+…+a_n^n < 1+n(n-1)/2*a_n^2
所以0 0,即n^(1/n)->1