观察 1/1*2+1/2*3==(1-1/2)+(1/2-1/3)=1-1/3=2/3 ,计算2/(x+1)(x+3)+2/(x+3)(x+5)+...+2/(x+2003)(x+2005)观察 1/1*2+1/2*3=(1-1/2)+(1/2-1/3)=1-1/3=2/3 , 计算2/(x+1)(x+3)+2/(x+3)(x+5)+...+2/(x+2003)(x+2005)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 02:33:31
![观察 1/1*2+1/2*3==(1-1/2)+(1/2-1/3)=1-1/3=2/3 ,计算2/(x+1)(x+3)+2/(x+3)(x+5)+...+2/(x+2003)(x+2005)观察 1/1*2+1/2*3=(1-1/2)+(1/2-1/3)=1-1/3=2/3 , 计算2/(x+1)(x+3)+2/(x+3)(x+5)+...+2/(x+2003)(x+2005)](/uploads/image/z/6849367-7-7.jpg?t=%E8%A7%82%E5%AF%9F+1%2F1%2A2%2B1%2F2%2A3%3D%3D%281-1%2F2%29%2B%281%2F2-1%2F3%29%3D1-1%2F3%3D2%2F3+%2C%E8%AE%A1%E7%AE%972%2F%28x%2B1%29%28x%2B3%29%2B2%2F%28x%2B3%29%28x%2B5%29%2B...%2B2%2F%28x%2B2003%29%28x%2B2005%29%E8%A7%82%E5%AF%9F+1%2F1%2A2%2B1%2F2%2A3%3D%281-1%2F2%29%2B%281%2F2-1%2F3%29%3D1-1%2F3%3D2%2F3+%2C+%E8%AE%A1%E7%AE%972%2F%28x%2B1%29%28x%2B3%29%2B2%2F%28x%2B3%29%28x%2B5%29%2B...%2B2%2F%28x%2B2003%29%28x%2B2005%29)
观察 1/1*2+1/2*3==(1-1/2)+(1/2-1/3)=1-1/3=2/3 ,计算2/(x+1)(x+3)+2/(x+3)(x+5)+...+2/(x+2003)(x+2005)观察 1/1*2+1/2*3=(1-1/2)+(1/2-1/3)=1-1/3=2/3 , 计算2/(x+1)(x+3)+2/(x+3)(x+5)+...+2/(x+2003)(x+2005)
观察 1/1*2+1/2*3==(1-1/2)+(1/2-1/3)=1-1/3=2/3 ,计算2/(x+1)(x+3)+2/(x+3)(x+5)+...+2/(x+2003)(x+2005)
观察 1/1*2+1/2*3=(1-1/2)+(1/2-1/3)=1-1/3=2/3 , 计算2/(x+1)(x+3)+2/(x+3)(x+5)+...+2/(x+2003)(x+2005)
观察 1/1*2+1/2*3==(1-1/2)+(1/2-1/3)=1-1/3=2/3 ,计算2/(x+1)(x+3)+2/(x+3)(x+5)+...+2/(x+2003)(x+2005)观察 1/1*2+1/2*3=(1-1/2)+(1/2-1/3)=1-1/3=2/3 , 计算2/(x+1)(x+3)+2/(x+3)(x+5)+...+2/(x+2003)(x+2005)
2/(x+1)(x+3)=1/(x+1)-1/(x+3).
2/(x+3)(x+5)=1/(x+3)-1/(x+5).
2/(x+5)(x+7)=1/(x+5)-1/(x+7).
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2/(x+2001)(x+2003)=1/(x+2001)-1/(x+2003).
2/(x+2003)(x+2005)=1/(x+2003)-1/(x+2005).
将以上的全部相加,
则可以得出答案:1/(x+1)-1/(x+2005).
即2004/(x+1)(x+2005)
=2*(1/(x+1)-1/(x+3)+(1/x+3)-1/(x+5)+...+(1/x+2003)-1/(x+2005))=2*(1/(x+1)-1/(x+2005))
=(4008/(x+1)*(x+2005)
2004/(x+1)*(x+2005)