计算:1/x(x+3)+1/(x+3)(x+6)+...+1/(x+2004)(x+2007)
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计算:1/x(x+3)+1/(x+3)(x+6)+...+1/(x+2004)(x+2007)
![计算:1/x(x+3)+1/(x+3)(x+6)+...+1/(x+2004)(x+2007)](/uploads/image/z/19333440-0-0.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9A1%2Fx%28x%2B3%29%2B1%2F%28x%2B3%29%28x%2B6%29%2B...%2B1%2F%28x%2B2004%29%28x%2B2007%29)
1/x(x+3)+1/(x+3)(x+6)+...+1/(x+2004)(x+2007)
=(1/3)[1/x-1/(x+3)+1/(x+3)-1/(x+6)+---+1/(x+2004)-1/(x+2007)]
=(1/3)[1/x-1/(x+2007)]
=669/(x^2+2007x)
=(1/3)[1/x-1/(x+3)+1/(x+3)-1/(x+6)+---+1/(x+2004)-1/(x+2007)]
=(1/3)[1/x-1/(x+2007)]
=669/(x^2+2007x)
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