(1/1*4)+(1/4*7)+(1/4*10)+.+(1/2008*2011)

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(1/1*4)+(1/4*7)+(1/4*10)+.+(1/2008*2011)
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(1/1*4)+(1/4*7)+(1/4*10)+.+(1/2008*2011)
(1/1*4)+(1/4*7)+(1/4*10)+.+(1/2008*2011)

(1/1*4)+(1/4*7)+(1/4*10)+.+(1/2008*2011)
(1/1*4)+(1/4*7)+(1/4*10)+.+(1/2008*2011)
=(1/3)×(1-1/4)+(1/3)×(1/4-1/7)+...+(1/3)×(1/2008-1/2011)
=(1/3)×(1-1/4+1/4-1/7+...+1/2008-1/2011)
=(1/3)×(1-1/2011)
=(1/3)×(2010/2011)
=670/2011;
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