题意得：limxn=a存在N对任意t>0 当n>N时 有|xn-a|则|xn^(1/3)-a^(1/3)|=|xn-a|/[xn^(2/3)+(xna)^(1/3)+a^(2/3)]=|xn-a|/{[xn^(1/3)+a^(1/3)/2]^2+3a^(2/3)/4}a-t<|xn-a|/[3a^(2/3)/4]即对任意t0>0选取t=[3a^(2/3)/4]t0>0存在N当n>N时 有|xn-a|从而|xn^(1/3)-a^(1/3)|∴limxn^(1/3)=a^(1/3)
