(1-1/2001)+(1-2/2001)+(1-3/2001)+······+(1-1999/2001)+(1-2000/2001)

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(1-1/2001)+(1-2/2001)+(1-3/2001)+······+(1-1999/2001)+(1-2000/2001)(1-1/2001)+(1-2/2001)+(1-3/2001)+

(1-1/2001)+(1-2/2001)+(1-3/2001)+······+(1-1999/2001)+(1-2000/2001)
(1-1/2001)+(1-2/2001)+(1-3/2001)+······+(1-1999/2001)+(1-2000/2001)

(1-1/2001)+(1-2/2001)+(1-3/2001)+······+(1-1999/2001)+(1-2000/2001)
(1-1/2001)+(1-2/2001)+(1-3/2001)+······+(1-1999/2001)+(1-2000/2001)
=2000-1/2000×(1+2+3+……+1999+2000)
=2000-1/2000×(1+2000)×2000/2
=2000-1000.5
=999.5
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