(1-1/2004)+(2-1/2004*2)+(3-1/2004*3)+.+(2004-1/2004*2004)这道题怎么做

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(1-1/2004)+(2-1/2004*2)+(3-1/2004*3)+.+(2004-1/2004*2004)这道题怎么做

(1-1/2004)+(2-1/2004*2)+(3-1/2004*3)+.+(2004-1/2004*2004)这道题怎么做
(1-1/2004)+(2-1/2004*2)+(3-1/2004*3)+.+(2004-1/2004*2004)
这道题怎么做

(1-1/2004)+(2-1/2004*2)+(3-1/2004*3)+.+(2004-1/2004*2004)这道题怎么做
(1-1/2004)+(2-1/2004*2)+(3-1/2004*3)+.+(2004-1/2004*2004)
=
(1-1/2004)+2×(1-1/2004)+3×(1-1/2004)+.+2004×(1-1/2004)
=（1+2+...+2004）×(1-1/2004)
=（1+2004）×2004÷2×2003/2004
=2005×2003÷2
=2008007.5