1/1x2+1/2x3+1/3x4+.+1/n(n+1)
=1-1/2+1/2-1/3+1/3-1/4+···+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)看我补充，谢谢1/2x4+1/4x6+1/6x8+…+1/2010x2012=1/2(2/2x4+2/4x6+2/6x8+···+2/2010x2012)=1/2(1/2-1/4+1/4-1/6+1/6-1/8+···+1/2010-1/2012)=1/2(1/2-1/2012)=1/2x2011/2024=2011/4048