如果|ab-2|+(b-1)²=0试求:1/ab+1/(a+1)×(b+1)+1/(a+2)×(b+2)+..
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如果|ab-2|+(b-1)²=0试求:1/ab+1/(a+1)×(b+1)+1/(a+2)×(b+2)+...+1/(a+2008)×(b+2008)的值.
![如果|ab-2|+(b-1)²=0试求:1/ab+1/(a+1)×(b+1)+1/(a+2)×(b+2)+..](/uploads/image/z/10265976-0-6.jpg?t=%E5%A6%82%E6%9E%9C%7Cab-2%7C%2B%28b-1%29%26%23178%3B%3D0%E8%AF%95%E6%B1%82%3A1%2Fab%2B1%2F%28a%2B1%29%C3%97%28b%2B1%29%2B1%2F%EF%BC%88a%2B2%EF%BC%89%C3%97%EF%BC%88b%2B2%EF%BC%89%2B..)
=2009/2012
绝对值和平方大于等于0,相加等于0,
所以两个都等于0
所以ab-2=0,b-1=0
b=1,a=2
所以原式=1/1×2+1/2×3+……+1/2009×2010
=1-1/2+1/2-1/3+……+1/2009-1/2010
=1-1/2010
=2009/2010
绝对值和平方大于等于0,相加等于0,
所以两个都等于0
所以ab-2=0,b-1=0
b=1,a=2
所以原式=1/1×2+1/2×3+……+1/2009×2010
=1-1/2+1/2-1/3+……+1/2009-1/2010
=1-1/2010
=2009/2010
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