2.计算1/(1*2*3)+1/(2*3*4)+1/(3*4*5？
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1/(1*2*3)+1/(2*3*4)+1/(3*4*5)
=1/6+1/24+1/60
=20/120+5/120+2/120
=27/60
=9/20
=1/6+1/24+1/60
=20/120+5/120+2/120
=27/60
=9/20
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1/(1x2x3)+1/(2x3x4)+1/(3x4x5)
= (1/2){ [1/(1x2)-1/(2x3)] + [1/(2x3)-1/(3x4)] + [1/(3x4)-1/(4x5)] }
= (1/2) [1/(1x2)-1/(4x5)]
= (1/2) (1/2-1/20)
= (1/2) (9/20)
=9/40
= (1/2){ [1/(1x2)-1/(2x3)] + [1/(2x3)-1/(3x4)] + [1/(3x4)-1/(4x5)] }
= (1/2) [1/(1x2)-1/(4x5)]
= (1/2) (1/2-1/20)
= (1/2) (9/20)
=9/40
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1/(1x2x3)+1/(2x3x4)+1/(3x4x5)
= (1/2){ [1/(1x2)-1/(2x3)] + [1/(2x3)-1/(3x4)] + [1/(3x4)-1/(4x5)] }
= (1/2) [1/(1x2)-1/(4x5)]
= (1/2) (1/2-1/20)
= (1/2) (9/20)
=9/40
= (1/2){ [1/(1x2)-1/(2x3)] + [1/(2x3)-1/(3x4)] + [1/(3x4)-1/(4x5)] }
= (1/2) [1/(1x2)-1/(4x5)]
= (1/2) (1/2-1/20)
= (1/2) (9/20)
=9/40
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=1/6+1/12+1/60=10/60十5/60十1/60=16/60
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4*5/1*2*3*4*5+5/2*3*4*5
+2/2*3*4*5=(20+5+2)/120=
27/120=9/40
+2/2*3*4*5=(20+5+2)/120=
27/120=9/40
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