1/10×11+1/11×12+…+1/19×20(要简算)

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1/10×11+1/11×12+…+1/19×20
(要简算)

1/10×11+1/11×12+…+1/19×20
=1/10-1/11+1/11-1/12+...+1/19-1/20
=1/10-1/20
=1/20

1/10×11+1/11×12+…+1/19×20
=1/10-1/11+1/11-1/12+1/12/-1/13+……1/19-1/20
=1/10-1/20
=1/20

通式1/[a*(a+1)]=1/a-1/(a+1)
原式=1/10-1/20=1/20

1/10×11+1/11×12+…+1/19×20
=1/10×(10+1)+1/11×(11+1)+…+1/19×(19+1)
=1+1/10+1+1/11+…+1+1/19
=10+1/10+1/11+…+1/19
后面的还在思考中……待续~~

原式=1/10(10+1)+1/11(11+1)+…+1/19(19+1)=(1+1/10)+(1+1/11)+…+(1+1/19)=(1+1+…+1)+(1/10+1/11+…+1/19)约=10+0.71877=10.71877