如果有理数a和b满足|ab-2|+|1-b|=0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+..
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如果有理数a和b满足|ab-2|+|1-b|=0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2004)(b+2004)的值
请说出原因,
请说出原因,
![如果有理数a和b满足|ab-2|+|1-b|=0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+..](/uploads/image/z/11560960-64-0.jpg?t=%E5%A6%82%E6%9E%9C%E6%9C%89%E7%90%86%E6%95%B0a%E5%92%8Cb%E6%BB%A1%E8%B6%B3%7Cab-2%7C%2B%7C1-b%7C%3D0%2C%E8%AF%95%E6%B1%821%2Fab%2B1%2F%EF%BC%88a%2B1%29%28b%2B1%29%2B1%2F%28a%2B2%29%28b%2B2%EF%BC%89%2B..)
|ab-2|+|1-b|=0因为绝对值是非负数,故b=1,a=2.
原题转化为,1/2+1/6+1/12+...+1/2005*2006
1/2=1-1/2;1/6=1/2-1/3;1/12=1/3-1/4.1/2005*2006=1/2005-1/2006.
原式等于1-1/2006=2005/2006
原题转化为,1/2+1/6+1/12+...+1/2005*2006
1/2=1-1/2;1/6=1/2-1/3;1/12=1/3-1/4.1/2005*2006=1/2005-1/2006.
原式等于1-1/2006=2005/2006
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