230问答网 > 1⼀1x2x3x4+1⼀2x3x4x5+1⼀3x4x5x6+1⼀4x5x6x7+1⼀5x6x7x8+1⼀6x7x8x9+1⼀7x8x9x10 求简算

1⼀1x2x3x4+1⼀2x3x4x5+1⼀3x4x5x6+1⼀4x5x6x7+1⼀5x6x7x8+1⼀6x7x8x9+1⼀7x8x9x10 求简算

2024-12-16 14:08:05

推荐回答（1个）

回答1：

1/(1×2×3×4)+1/(2×3×4×5)+1/(3×4×5×6)+...+1/(7×8×9×10)
=(1/3)×［1/(1×2×3)-1/(2×3×4)］+(1/3)×［1/(2×3×4)-1/(3×4×5)］+(1/3)×［1/(3×4×5)-1/(4×5×6)］+...+(1/3)×［1/(7×8×9)-1/(8×9×10)］
=(1/3)×［1/(1×2×3)-1/(2×3×4)+1/(2×3×4)-1/(3×4×5)+1/(3×4×5)-1/(4×5×6)+...+1/(7×8×9)-1/(8×9×10)］
=(1/3)×［1/(1×2×3)-1/(8×9×10)］
=(1/3)×［(1/6)-(1/720)］
=(1/3)×(119/720)
=119/2160