Question

证明lim(n→∝)n的负k次方等于零,k大于零

Answer 1

考虑

|n^(-k)-0|

=1/n^k

对任意ε>0,现在要1/n^k1/ε

n>(1/ε)^(1/k)

取N=[(1/ε)^(1/k)]+1>0,当n>N,就有|n^(-k)-0|