lim[1/(1*4)+1/(4*7).+1/(3n-1)(3n+1)]我怎么觉得题目有错阿,
问题描述:
lim[1/(1*4)+1/(4*7).+1/(3n-1)(3n+1)]我怎么觉得题目有错阿,
答
裂项法,原式
=lim 1/3 * (1 - 1/4 + 1/4 - 1/7 + ...+ 1/(3n-1) - 1/(3n+1 ) )
=lim 1/3 * (1 - 1/(3n+1) )
=lim n/(3n+1)
=1/3