1/1x2x3+1/2x3x4+1/3x4x5+.+1/n(n+1)(n+2)

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/11/09 03:36:34

Sn=1/[n(n+1)(n+2)]=(1/2){1/[n)n+1)]-1/[(n+1)(n+2)]}
=(1/2)[1/n-1/(n+1)-1/(n+1)+1/(n+2)]
=(1/2)[1/n-2/(n+1)+1/(n+2)]
=1/1x2x3+1/2x3x4+1/3x4x5+...+1x/n(n+1)(n+2)
=(1/2)[1/1-2/2+1/3+1/2-2/3+1/4+1/3-2/4+1/5+/4-2/5+1/6
+.+1/n-2/(n+1)+1/(n+2)]
=(1/2)[1-1/2-1/(n+1)+1/(n+2)]
=(n^2+3n)/[4(n+1)(n+2)]

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