如果有理数,a,b满足|ab-2|+|1-b|=0,求ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1
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如果有理数,a,b满足|ab-2|+|1-b|=0,求ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1+...+(a+2003)(b+2003)的值
写出算式
写出算式
![如果有理数,a,b满足|ab-2|+|1-b|=0,求ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1](/uploads/image/z/17487343-55-3.jpg?t=%E5%A6%82%E6%9E%9C%E6%9C%89%E7%90%86%E6%95%B0%2Ca%2Cb%E6%BB%A1%E8%B6%B3%7Cab-2%7C%2B%7C1-b%7C%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%28a%2B2%29%28b%2B2%29%E5%88%86%E4%B9%8B1)
|ab-2|+|1-b|=0 则|ab-2|=0 |1-b|=0 b=1 a=2
ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1+...+(a+2003)(b+2003)
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+.+1/(2004*2005)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+.1/2004-1/2005
=1-1/2005
=2004/2005
方法:中间对消,开头减结尾
ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1+...+(a+2003)(b+2003)
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+.+1/(2004*2005)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+.1/2004-1/2005
=1-1/2005
=2004/2005
方法:中间对消,开头减结尾
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