几个极限的证明

(求证：lim_{n o infty }frac{1}{n^alpha}=0,alpha>0)
(证明：)
(分为两种情况考虑，情况1：alpha>=1,情况2：alpha<1)
(情况1：当alphageq 1)
(|frac{1}{n^alpha}-0|=frac{1}{n^alpha}<frac{1}{n})
(若需frac{1}{n}<epsilon)
(即n>frac{1}{epsilon},即可)
(即，取N=[frac{1}{epsilon}]+1)
(则当quad n>N时，即有quad frac{1}{n} < frac{1}{N}<epsilon)