是 an=1/(n+1)+1/(n+2)+.+1/(2n) 就依此帮你解答.
因为 a(n+1)-an=[1/(n+2)+1/(n+3)+.1/(2n+2)] - [1/(n+1)+1/(n+2)+.+1/(2n)]
=1/(2n+1)+1/(2n+2)-1/(n+1)
=1/[2(n+1)(2n+1)]
>0 ,
所以数列的后项比前项大,即该数列是递增数列 .