已知根号a-1+(ab-2)²=0,求ab分之1+(a+1)(b+1)分之1+++(a+2004)(b+200
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已知根号a-1+(ab-2)²=0,求ab分之1+(a+1)(b+1)分之1+++(a+2004)(b+2004)分之1的值
![已知根号a-1+(ab-2)²=0,求ab分之1+(a+1)(b+1)分之1+++(a+2004)(b+200](/uploads/image/z/2147875-43-5.jpg?t=%E5%B7%B2%E7%9F%A5%E6%A0%B9%E5%8F%B7a-1%2B%28ab-2%29%26sup2%3B%3D0%2C%E6%B1%82ab%E5%88%86%E4%B9%8B1%2B%28a%2B1%29%28b%2B1%29%E5%88%86%E4%B9%8B1%2B%2B%2B%EF%BC%88a%2B2004%29%28b%2B200)
√(a-1)+(ab-2)²=0
所以a-1=0 ab-2=0
a=1 b=2
ab分之1+(a+1)(b+1)分之1+++(a+2004)(b+2004)分之1
=1/(1×2)+1/(2×3)+1/(3×4)+……1/(2005×2006)
=1/2+1/2-1/3+1/3-1/4+……+1/2005-1/2006
=1-1/2006
=2005/2006
所以a-1=0 ab-2=0
a=1 b=2
ab分之1+(a+1)(b+1)分之1+++(a+2004)(b+2004)分之1
=1/(1×2)+1/(2×3)+1/(3×4)+……1/(2005×2006)
=1/2+1/2-1/3+1/3-1/4+……+1/2005-1/2006
=1-1/2006
=2005/2006
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