使不等式1/n(n+1)+1/(n+1)(n+2)+...+1/(2n-1)2n

问题描述:

使不等式1/n(n+1)+1/(n+1)(n+2)+...+1/(2n-1)2n

1/n(n+1)+1/(n+1)(n+2)+...+1/(2n-1)2n
=1/n-1/(n+1)+1/(n+1)-1/(n+2)+...+1/(2n-1)-1/2n
=1/n-1/2n
=1/2n=1
则0