1/1*2+1/2*3+1/4*5+……+1/2004*2005
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![1/1*2+1/2*3+1/4*5+……+1/2004*2005](/uploads/image/z/1668512-56-2.jpg?t=1%2F1%2A2%2B1%2F2%2A3%2B1%2F4%2A5%2B%E2%80%A6%E2%80%A6%2B1%2F2004%2A2005)
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1/1*2+1/2*3+1/4*5+……+1/2004*2005
1/1*2+1/2*3+1/4*5+……+1/2004*2005
1/1*2+1/2*3+1/4*5+……+1/2004*2005
2004\2005
可以化成
1-1/2+1/2-1/3+1/3.+1/2004-1/2005
=1-1/2005
=2004/2005