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1/(x+1)(x十2)+1/(x+2)(x十3)十…十1/(x十2o02)(x+20o3)=2十4003/3x+6oo9
题目详情
1/(x+1)(x十2)+1/(x+2)(x十3)十…十1/(x十2o02)(x+20o3)=2
十4003/3x+6oo9
十4003/3x+6oo9
▼优质解答
答案和解析
1/(x+1)(x十2)+1/(x+2)(x十3)十…十1/(x十2o02)(x+20o3)=2+4003/(3x+6009),拆项得
1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+.+1/(x+2002)-1/(x+2003)
= 1/(x+1)-1/(x+2003) = 2+4003/(3x+6009),
1/(x+1)-2 = 4003/(3x+6009)+3(3x+6009),
-(2x+1)/(x+1) = 4006/(3x+6009)
(2x+1)(3x+6009)+4006(x+1)=0
6x^2+12021x+6009+4006x+4006=0
6x^2+16027x+10015=0
解之即可
1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+.+1/(x+2002)-1/(x+2003)
= 1/(x+1)-1/(x+2003) = 2+4003/(3x+6009),
1/(x+1)-2 = 4003/(3x+6009)+3(3x+6009),
-(2x+1)/(x+1) = 4006/(3x+6009)
(2x+1)(3x+6009)+4006(x+1)=0
6x^2+12021x+6009+4006x+4006=0
6x^2+16027x+10015=0
解之即可
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