1/1x2x3+1/2x3x4+1/3x4x5+.+1/9x10x11=

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/02 03:27:10

1/n(n+1)(n+2)=1/2*[1/n-2/(n+1)+1/(n+2)]
原式=1/2*(1-2*1/2+1/3+1/2-2*1/3+1/4+.+1/9-2*1/10+1/11)
=1/2*(1-1/2-1/10+1/11)=27/110

1/1x2x3+1/2x3x4+1/3x4x5+.+1/9x10x11= 1x2X3+2x3X4+3x4X5+…+7X8X9=? 1x2x3+2x3x4+3x4x5+...+7x8x9=, 1/1x2x3+1/2x3x4+1/3x4x5 1x2x3+2x3x4+3x4x5+…+8x9x10 1x2x3+2x3x4+3x4x5+.+10x11x12 1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+.+1/48x49x50= 1/1x2x3+1/2x3x4+1/3x4x5+.+1/11x12x13= 请1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6= 1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+.1/(20x21x22)=? 1/1x2x3+1/2x3x4+1/3x4x5+.1/98x99x100= 1x2x3+2x3x4+3x4x5+4x5x6+...+n(n+1)(n+2)=