已知|ab-2|与(b-1)2次方互为相反数,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+2006)(b+2006)的值
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![已知|ab-2|与(b-1)2次方互为相反数,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+2006)(b+2006)的值](/uploads/image/z/10062710-62-0.jpg?t=%E5%B7%B2%E7%9F%A5%7Cab-2%7C%E4%B8%8E%28b-1%292%E6%AC%A1%E6%96%B9%E4%BA%92%E4%B8%BA%E7%9B%B8%E5%8F%8D%E6%95%B0%2C%E6%B1%821%2Fab%2B1%2F%28a%2B1%29%28b%2B1%29%2B1%2F%28a%2B2%29%28b%2B2%29%2B...1%2F%28a%2B2006%29%28b%2B2006%29%E7%9A%84%E5%80%BC)
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已知|ab-2|与(b-1)2次方互为相反数,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+2006)(b+2006)的值
已知|ab-2|与(b-1)2次方互为相反数,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+2006)(b+2006)的值
已知|ab-2|与(b-1)2次方互为相反数,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+2006)(b+2006)的值
|ab-2|>=0
(b-1)^2>=0
|ab-2|与(b-1)^2互为相反数
则
|ab-2|=(b-1)^2=0
ab-2=0
b-1=0
a=2
b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+2006)(b+2006)
=1/2*1+1`/(2+1)(1+1)+1/(2+2)(1+2)+.+1/(2+2006)(1+2006)
=1/1*2+1/2*3+1/3*4+.+1/2007*2008
=1-1/2+1/2-1/3+1/3-1/4+.+1/2007-1/2008
=1-1/2008
=2007/2008
因为二者大于等于0,又因为互为相反数,所以二者等于0。所以b=1,所以a=2。所以原式得1/2+1/(3*2)+1/(4*3)+...+1/(2007*20006)=1/2+1/2-1/3+1/3-1/4....+1/2005-1/2006+1/2006-1/2007=1-1/2007=2006/2007