1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+...+1/8x9x10 等于多少?

来源：学生作业帮助网编辑：作业帮时间：2024/05/04 01:13:46

1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+...+1/8x9x10 等于多少?
1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+...+1/8x9x10 等于多少?

1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+...+1/8x9x10 等于多少?
1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+...+1/8x9x10
=1-1/2-1/2(1-1/3)
+1/2-1/3-1/2(1/2-1/4)
+1/3-1/4-1/2(1/3-1/5)
+1/4-1/5-1/2(1/4-1/6)
+.
+1/8-1/9-1/2(1/8-1/10)
=1-1/9-1/2(1+1/2-1/9-1/10)
=173/360

原式=1/2×（1/1×2-1/2×3+1/2×3-1/3×4+……+1/8×9-1/9×10）
=1/2×（1/1×2-1/9×10）
=11/45

答案是2/9，主要是运用拆项运算。

1x2x3+2x3x4+...+nxx=? 1x2=1/3x(1x2x3-0x1x2)2x3=1/3x(2x3x4-1x2x3)3x4=1/3x(3x4x5-2x3x4)求1x2x3+2x3x4+3x4x5+...+7x8x9=? 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 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) 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=? 1/1x2x3+1/2x3x4+1/3x4x51/2x3x4 + 1/3x4x5 + 1/4x5x6 +……+1/99x100x101是 1/（2x3x4）