1/1*4+1/4*7+1/7*10+...+1/2008*2010

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1/1*4+1/4*7+1/7*10+...+1/2008*20101/1*4+1/4*7+1/7*10+...+1/2008*20101/1*4+1/4*7+1/7*10+...+1/2008*20

1/1*4+1/4*7+1/7*10+...+1/2008*2010
1/1*4+1/4*7+1/7*10+...+1/2008*2010

1/1*4+1/4*7+1/7*10+...+1/2008*2010
1/(1×4)+1/(4×7)+1/(7×10)+……+1/(2008×2010)
=(1/3)×[3/(1×4)+3/(4×7)+3/(7×10)+……+3/(2008×2010)]
=(1/3)×[(4-1)/(1×4)+(7-4)/(4×7)+(10-7)/(7×10)+……+(2010-2008)/(2008×2010)]
=(1/3)×(1/1-1/4+1/4-1/7+1/7-1/10+……+1/2008-1/2010)
=(1/3)×(1-1/2010)
=2009/6030