3分之1加上15分之1加上35分之1加上省略号加上2009乘以2011分之1，等于多少

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1/(1*3)=(1/1-1/3)*(1/2)
1/(3*5)=(1/3-1/5)*(1/2)
......
1/(2009*2011)=(1/2009-1/2011)*(1/2)

所以1/毕悄(1*3)+1/拿数晌(3*5)+...+1/(2009*2011)=(1/2)*(1/消锋1-1/3+1/3-1/5+...+1/2009-1/2011)
=(1/2)*(1/1-1/2011)
=(1/2)*(2010/2011)
=1005/2011

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