已知|ab-2|与|b-1|互为相反数,试求代数式1 1 1 1—+ ---------- + ---------- + .+ ----------------的值ab (a+1)(b+1) (a+2)(b+2) (a+2007)(b+2007)1 1 1
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![已知|ab-2|与|b-1|互为相反数,试求代数式1 1 1 1—+ ---------- + ---------- + .+ ----------------的值ab (a+1)(b+1) (a+2)(b+2) (a+2007)(b+2007)1 1 1](/uploads/image/z/3962554-34-4.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++++++++1++++++++++++1++++++++++++++++++++++++1%E2%80%94%2B+----------+%2B+----------+%2B+.%2B+----------------%E7%9A%84%E5%80%BCab++%28a%2B1%29%28b%2B1%29+++%28a%2B2%29%28b%2B2%29+++++++++++%28a%2B2007%29%28b%2B2007%291++++++1+++++++++++++1)
已知|ab-2|与|b-1|互为相反数,试求代数式1 1 1 1—+ ---------- + ---------- + .+ ----------------的值ab (a+1)(b+1) (a+2)(b+2) (a+2007)(b+2007)1 1 1
已知|ab-2|与|b-1|互为相反数,试求代数式
1 1 1 1
—+ ---------- + ---------- + .+ ----------------的值
ab (a+1)(b+1) (a+2)(b+2) (a+2007)(b+2007)
1 1 1 1
—+ ---------- + ---------- + ......+ ----------------的值
ab (a+1)(b+1) (a+2)(b+2) (a+2007)(b+2007)
已知|ab-2|与|b-1|互为相反数,试求代数式1 1 1 1—+ ---------- + ---------- + .+ ----------------的值ab (a+1)(b+1) (a+2)(b+2) (a+2007)(b+2007)1 1 1
|ab-2|与|b-1|互为相反数
|ab-2|+|b-1|=0
|ab-2|,|b-1|都为非负数,两者和为0.两者必定都为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+2007)(b+2007)
=1/2*1+1/3*2+1/4*3+.+1/2009*2008
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2008-1/2009)
=1-1/2009
=2008/2009