若极限LIM[(3N+1)*AN]=1,求LIM(NAN)的极限 答案为1/3.

问题描述:

若极限LIM[(3N+1)*AN]=1,求LIM(NAN)的极限 答案为1/3.

由于3n+1→∞,而要使lim (3n+1)an存在,必有an→0
所以 lim(3n+1)an = lim 3nan + lim an
=3lim nan +0
=3lim nan
=1
得到lim nan = 1/3