求:1/1×2+1/2×3+1/3×4+……1/8×9+1/9×10的解题过程

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求:1/1×2+1/2×3+1/3×4+……1/8×9+1/9×10的解题过程

求:1/1×2+1/2×3+1/3×4+……1/8×9+1/9×10的解题过程
求:1/1×2+1/2×3+1/3×4+……1/8×9+1/9×10的解题过程

求:1/1×2+1/2×3+1/3×4+……1/8×9+1/9×10的解题过程
1/(1×2)+1/(2×3)+1/(3×4)+...+1/(8×9)+1/(9×10)
=1-1/2+1/2-1/3+1/3-1/4+...+1/8-1/9+1/9-1/10
=1-1/10
=9/10

1/1×2+1/2×3+1/3×4+……1/8×9+1/9×10
=1-1/2+1/2-1/3+1/3-1/4+......+1/9-1/10
=1-1/10
=9/10