用ε-N定义证明lim(n→∞)(√n+1)⼀(3√n-1)=1⼀3

2024-11-29 03:45:57
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回答(1):

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