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+2013)(b+2013)的值
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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+2013)(b+2013)的值](/uploads/image/z/3813362-26-2.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%E2%80%A6%2B1%2F%28a%2B2013%29%28b%2B2013%29%E7%9A%84%E5%80%BC)
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+2013)(b+2013)的值
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+2013)(b+2013)的值
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+2013)(b+2013)的值
∵|ab-2|与|b-1|互为相反数
∴|ab-2|+|b-1|=0
ab-2=0 b-1=0
∴b=1
a=2
∴1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2013)(b+2013)
=1/1*2+1/2*3+1/3*4+1/4*5+.+1/2013*2014
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/2013-1/2014
=1-1/2014
=2013/2014