1*2/1+2*3/1+3*4/1+4*5/1···2005*2006/1
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1*2/1+2*3/1+3*4/1+4*5/1···2005*2006/1
1*2/1+2*3/1+3*4/1+4*5/1···2005*2006/1
1*2/1+2*3/1+3*4/1+4*5/1···2005*2006/1
是不是1/(1*2)+1/(2*3)+...+1/(2005*2006)?是的话注意1/(1*2)=1/1-1/2..1/(2005*2006)=1/2005-1/2006 所以原式就等于1/1-1/2006=2005/2006