如果有理数a,b满足|ab-2|+(1-b)^2=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)…+
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如果有理数a,b满足|ab-2|+(1-b)^2=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)…+1/(a+2007)(b+2007)的值:
![如果有理数a,b满足|ab-2|+(1-b)^2=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)…+](/uploads/image/z/5591707-43-7.jpg?t=%E5%A6%82%E6%9E%9C%E6%9C%89%E7%90%86%E6%95%B0a%2Cb%E6%BB%A1%E8%B6%B3%7Cab-2%7C%2B%281-b%29%5E2%3D0%2C%E6%B1%821%2Fab%2B1%2F%28a%2B1%29%28b%2B1%29%2B1%2F%28a%2B2%29%28b%2B2%29%E2%80%A6%2B)
由已知得b=1 a=2
所以式子等于1/(1*2)+1/(2*3)+1/(3*4)+.+1/(2008*2009)=
(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2008-1/2009)=2008/2009
所以式子等于1/(1*2)+1/(2*3)+1/(3*4)+.+1/(2008*2009)=
(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2008-1/2009)=2008/2009
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