1/(x+1)(x+2)+1/(x+2)(x+3)+、、、+1/（x+2003）（x+2004）=1/3x+6012
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1/(x+1)(x+2)+1/(x+2)(x+3)+、、、+1/（x+2003）（x+2004）=1/3x+60121/(x+1)(x+2)+1/(x+2)(x+3)+、、、+1/（x+2003）（x
1/(x+1)(x+2)+1/(x+2)(x+3)+、、、+1/（x+2003）（x+2004）=1/3x+6012
1/(x+1)(x+2)+1/(x+2)(x+3)+、、、+1/（x+2003）（x+2004）=1/3x+6012
1/(x+1)(x+2)+1/(x+2)(x+3)+、、、+1/（x+2003）（x+2004）=1/3x+6012
1/(x+1)(x+2)+1/(x+2)(x+3)+、、、+1/（x+2003）（x+2004）
=1/(x+1)-1/(x+2)+1/x+2)-1/(x+3)+------+1/(x+2003)-1/(x+2004)
=1/(x+1)-1/(x+2004)
=2003/(x^2+2005x+2004)
=1/3x+6012
下面自己解吧,
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