1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+.+1/8x9x10 等于多少？急！
1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+...+1/8x9x10 等于多少？急！
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
1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+......+1/48x49x50=
1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+......+1/48x49x50=48*51÷(4*49*50)=306/1225
请1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6=
=1/2×(1/1×2-1/2×3+1/2×3-1/3×4+1/3×4-1/4×5+1/4×5-1/5×6)
=1/2×(1/1×2-1/5×6)
=7/30
1/1x2x3+1/2x3x4+1/3x4x5+............+1/9x10x11=
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
1/2X3X4+1/3X4X5+1/4X5X6+。。。。。。+1/99X100X101=?
原式＝1/2×（1/2*3-1/3*4+1/3*4-1/4*5+。。。。。+1/98*99-1/99*100）
＝1/2（1/2×3-1/99×100）
＝1/2×（1649-1）/9900
＝824/9900
＝206/2475
1/1x2x3+1/2x3x4+1/3x4x5
解1/(1+2+3)+1/(2+3+4)+1/(3+4+5)……+1/(99+100+101)
=1/6+1/9+1/12+1/15...........+1/300
=1/3*(1/2+1/3.....+1/99+1/100)
=1/3*4.18737751763961
=1.39579250587987
1/1x2x3+1/2x3x4+1/3x4x5+...........+1/n(n+1)(n+2)
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)]
1/1x2x3+1/2x3x4+1/3x4x5+....+1/11x12x13= （要过程）
原式=﹙1-1／2-1／3﹚+﹙1／2-1／3-1／4﹚+﹙1／3-1／4-1／5﹚+······+﹙1／11-1／12-13／13﹚=1-1／13=12／13
1/2X3X4X5+1/3X4X5X6+1/4X5X6X7......1/97X98X99X100=?
1/2X3X4X5+1/3X4X5X6+1/4X5X6X7......1/97X98X99X100=?
=1/3[1/2*3*4-1/3*4*5]+1/3[1/3*4*5-1/4*5*6]+1/3[1/4*5*6-1/5*6*7]+...+1/3[1/97*98*99-1/98*99*100]
=1/3[1/2*3*4-1/98*99*100]
=1/3*40424/98*99*100
=5053/3*49*99*25
1x2x3+2x3x4+3x4x5+…+8x9x10
解：
1×2×3+2×3×4+3×4×5+……+8×9×10
=(1/4)(1×2×3×4)+(1/4)(2×3×4×5-1×2×3×4)+(1/4)(3×4×5×6-2×3×4×5)+……(1/4)(8×9×10×11-7×8×9×10)
=(1/4)(1×2×3×4+2×3×4×5-1×2×3×4+3×4×5×6-2×3×4×5+……+8×9×10×11-7×8×9×10)
=(1/4)(8×9×10×11)
=2×9×10×11
=1980
