1/1*2+1/2*3+1/3*4+1/4*5...+1/2002*2003+1/2003*2004+1/2004*2005
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![1/1*2+1/2*3+1/3*4+1/4*5...+1/2002*2003+1/2003*2004+1/2004*2005](/uploads/image/z/217833-33-3.jpg?t=1%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%2B1%2F4%2A5...%2B1%2F2002%2A2003%2B1%2F2003%2A2004%2B1%2F2004%2A2005)
1/1*2+1/2*3+1/3*4+1/4*5...+1/2002*2003+1/2003*2004+1/2004*2005
1/1*2+1/2*3+1/3*4+1/4*5...+1/2002*2003+1/2003*2004+1/2004*2005
1/1*2+1/2*3+1/3*4+1/4*5...+1/2002*2003+1/2003*2004+1/2004*2005
1/n(n+1)=1/n-1/(n+1)
1/1*2+1/2*3+1/3*4+1/4*5...+1/2002*2003+1/2003*2004+1/2004*2005
=1/1-1/2+1/2-1/3+1/3-1/4+……+1/2003-1/2004+1/2004-1/2005
=1-1/2005
=2004/2005