1/1x2x3+1/2x3x4+1/3x4x5+.+1/8x9x10 求简算

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1/1x2x3+1/2x3x4+1/3x4x5+.+1/8x9x10 求简算
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1/1x2x3+1/2x3x4+1/3x4x5+.+1/8x9x10 求简算
1/1x2x3+1/2x3x4+1/3x4x5+.+1/8x9x10 求简算

1/1x2x3+1/2x3x4+1/3x4x5+.+1/8x9x10 求简算

1/1x2x3+1/2x3x4+1/3x4x5+......+1/8x9x10
=1/2 [1/1×2-1/2×3+1/2×3-1/3×4+1/3×4-1/4×5+。。。+1/8×9-1/9×10]
=1/2[1/2-1/90]
=1/2×44/90
=11/45