1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+...+1/8x9x10 等于多少?
问题描述：
1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+...+1/8x9x10 等于多少?
答
答案是2/9，主要是运用拆项运算。
答
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
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