求证1/1X2X3+1/2X3X4+...+1/n(n+1)(n+2)=n(n+3)/4(n+1)(n+2)

来源：学生作业帮助网编辑：六六作业网时间：2025/02/02 01:22:06

求证1/1X2X3+1/2X3X4+...+1/n(n+1)(n+2)=n(n+3)/4(n+1)(n+2)求证1/1X2X3+1/2X3X4+...+1/n(n+1)(n+2)=n(n+3)/4(n

求证1/1X2X3+1/2X3X4+...+1/n(n+1)(n+2)=n(n+3)/4(n+1)(n+2)
求证1/1X2X3+1/2X3X4+...+1/n(n+1)(n+2)=n(n+3)/4(n+1)(n+2)

求证1/1X2X3+1/2X3X4+...+1/n(n+1)(n+2)=n(n+3)/4(n+1)(n+2)
解.裂项法.
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)]
S=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)]
明教为您解答,
如果不能请追问,我会尽全力帮您解决的~
如果您有所不满愿意,请谅解~

1x2x3+2x3x4+...+nxx=? 1/1x2x3+1/2x3x4+.+1/98x99x100 . 1/1X2X3+1/2X3x4+…+1/48X49X50 1X2X3+2X3X4+.+n(n+1)(n+2) 1x2x3+2x3x4+.+nx(n+1)(n+2)=? 1x2x3+2x3x4+.+n(n+1)(n+2)=? 求和1x2x3+2x3x4+...+n(n+1)(n+2) 1x2x3+2x3x4+…+n(n+1) 1x2x3+2x3x4+3x4x5+…+8x9x10 1x2x3+2x3x4+3x4x5+.+10x11x12 1x2x3+2x3x4+3x4x5+...+7x8x9=, 1x2X3+2x3X4+3x4X5+…+7X8X9=? 1x2x3 2x3x4 3x4x5 .10x11x12,怎么算求和：1X2X3+2X3X4+3X4X5+...+98X99X100 计算1x2x3+2x3x4+…+48x49x50 1x2=1|3(1x2x3-0x1x2) 2x3=1|3(2x3x4-1x2x3) 3x4=1|3(3x4x5-2x3x4)由此推断1x2x3+2x3x4+3x4x5.7x8x9=? 1x2=1/3x(1x2x3-0x1x2)2x3=1/3x(2x3x4-1x2x3)3x4=1/3x(3x4x5-2x3x4)求1x2x3+2x3x4+3x4x5+...+7x8x9=? 1/1x2x3+1/2x3x4+1/3x4x51/2x3x4 + 1/3x4x5 + 1/4x5x6 +……+1/99x100x101是 1/（2x3x4）