1/1*3+1/2*4+1/3*5+...+1/2005*2007
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![1/1*3+1/2*4+1/3*5+...+1/2005*2007](/uploads/image/z/10096455-39-5.jpg?t=1%2F1%2A3%2B1%2F2%2A4%2B1%2F3%2A5%2B...%2B1%2F2005%2A2007)
1/1*3+1/2*4+1/3*5+...+1/2005*2007
1/1*3+1/2*4+1/3*5+...+1/2005*2007
1/1*3+1/2*4+1/3*5+...+1/2005*2007
题目是1/(1*3)+1/(2*4)+...
因为1/(1*3)=1/2*(1/1-1/3)
所以原式=1/2*(1/1-1/3)+1/2*(1/2-1/4)+1/2*(1/3-1/5)+1/2*(1/4-1/6)+...
=1/2*(1/1+1/2-1/2006-1/2007)