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3/2+7/6+13/12.2008x2009+1/2008x2009
题目详情
3/2+7/6+13/12.2008x2009+1/2008x2009
▼优质解答
答案和解析
(1*2+1)/(1*2)+(2*3+1)/(2*3)+(3*4+1)/(3*4)+……+(2008*2009+1)/(2008*2009)
=[1+1/(1*2)]+[1+1/(2*3)]+……[1+1/(2008*2009)]
=2008+1-1/2+1/2-1/3+1/3-1/4+……+1/2008-1/2009
=2008+1-1/2009
=2008+2008/2009
=[1+1/(1*2)]+[1+1/(2*3)]+……[1+1/(2008*2009)]
=2008+1-1/2+1/2-1/3+1/3-1/4+……+1/2008-1/2009
=2008+1-1/2009
=2008+2008/2009
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