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+2008)(b+2008)
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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+2008)(b+2008)](/uploads/image/z/5462615-47-5.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%EF%BC%88a%2B1%EF%BC%89%EF%BC%88b%2B1%EF%BC%89%2B1%2F%EF%BC%88a%2B2%EF%BC%89%EF%BC%88b%2B2%EF%BC%89%2B%E2%80%A6%2B1%2F%28a%2B2008%29%28b%2B2008%29)
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+2008)(b+2008)
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+2008)(b+2008)
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+2008)(b+2008)
|ab-2|与|b-1|互为相反数,因绝对值不可能为负数,所以 |ab-2|与|b-1|均为0,b=1,a=2.
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2008)(b+2008)
=1/1*2 + 1/2*3 + 1/3*4 + ...+ 1/2009*2010
=(1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + ...+ (1/2009 - 1/2010)
=1-1/2010
=2009/2010