1/1*2+1/2*3+1/3*4+.1/2001*2002+1/2002*2003
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![1/1*2+1/2*3+1/3*4+.1/2001*2002+1/2002*2003](/uploads/image/z/1561236-60-6.jpg?t=1%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%2B.1%2F2001%2A2002%2B1%2F2002%2A2003)
1/1*2+1/2*3+1/3*4+.1/2001*2002+1/2002*2003
1/1*2+1/2*3+1/3*4+.1/2001*2002+1/2002*2003
1/1*2+1/2*3+1/3*4+.1/2001*2002+1/2002*2003
1/1*2+1/2*3+1/3*4+.1/2001*2002+1/2002*2003
=1-1/2+1/2-1/3+1/3-1/4+……+1/2001-1/2002+1/2002-1/2003
=1-1/2003
=2002/2003