已知数列An=1/n=1+1/n=2+...+1/2n.求An是递增数列还是递减数列?谢谢·主要是方法哦

Question

已知数列An=1/n=1 +1/n=2 +...+1/2n.求An是递增数列还是递减数列?谢谢·主要是方法哦

Answer 1

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...