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](/uploads/image/z/1044356-68-6.jpg?t=1%2A2%2F1%2B2%2A3%2F1%2B3%2A4%2F1%2B4%2A5%2F1%C2%B7%C2%B7%C2%B72005%2A2006%2F1)
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