已知|ab-2|与|b-1|互为相反数,试求代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2012)1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2012)(b+2012)
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![已知|ab-2|与|b-1|互为相反数,试求代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2012)1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2012)(b+2012)](/uploads/image/z/7133851-19-1.jpg?t=%E5%B7%B2%E7%9F%A5%7Cab-2%7C%E4%B8%8E%7Cb-1%7C%E4%BA%92%E4%B8%BA%E7%9B%B8%E5%8F%8D%E6%95%B0%2C%E8%AF%95%E6%B1%82%E4%BB%A3%E6%95%B0%E5%BC%8F1%2Fab%2B1%2F%28a%2B1%29%28b%2B1%29%2B1%2F%28a%2B2%29%28b%2B2%29%2B.%2B1%2F%28a%2B2012%EF%BC%891%2Fab%2B1%2F%28a%2B1%29%28b%2B1%29%2B1%2F%28a%2B2%29%28b%2B2%29%2B.%2B1%2F%28a%2B2012%29%28b%2B2012%29)
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已知|ab-2|与|b-1|互为相反数,试求代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2012)1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2012)(b+2012)
已知|ab-2|与|b-1|互为相反数,试求代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2012)
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2012)(b+2012)
已知|ab-2|与|b-1|互为相反数,试求代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2012)1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2012)(b+2012)
|ab-2|+|b-1|=0
b-1=0 b=1
ab=2 a=2/b=2
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2012)(b+2012)
=1/1x2+1/2x3+1/3x4+...+1/2013x2014
=1-1/2+1/2-1/3+1/3-1/4+...+1/2013-1/2014
=1-1/2014
=2013/2014