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