1比2乘3+1比3乘4+1比4乘5+...+1比19乘20

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1比2乘3+1比3乘4+1比4乘5+...+1比19乘20
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1比2乘3+1比3乘4+1比4乘5+...+1比19乘20
1比2乘3+1比3乘4+1比4乘5+...+1比19乘20

1比2乘3+1比3乘4+1比4乘5+...+1比19乘20
1/(2×3)+1/(3×4)+1/(4×5)+……+1/(19×20)
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/19-1/20
=1/2-1/20
=10/20-1/20
=9/20

答:分数的裂项知识
1/(2*3)+1/(3*4)+...+1/(19*20)
=1/2-1/3+1/3-1/4+...+1/19-1/20
=1/2-1/20
=9/20