计算1/1X4+1X7+ 1/7x10+...+1 - 知识问答

计算1/1X4+1X7+ 1/7x10+...+1/2008X2011的值是多少

1个回答

1/(1×4)+1/(4×7)+1/(7×10)+…+1/(2008×2011)
= (1/3)×(1-1/4)+(1/3)×(1/4-1/7)+(1/3)×(1/7-1/10)+…+(1/3)×(1/2008-1/2011)
= (1/3)×[(1-1/4)+(1/4-1/7)+(1/7-1/10)+…+(1/2008-1/2011)]
= (1/3)×(1-1/2011)
= (1/3)×(2010/2011)
= 670/2011

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