已知/ab-2/与/b-1/互为相反数,试求代数式1/ab+1/(a+2)(b+2)+...+1/(a=2009)(b+2009)的值

已知/ab-2/与/b-1/互为相反数,试求代数式1/ab+1/(a+2)(b+2)+...+1/(a=2009)(b+2009)的值
已知/ab-2/与/b-1/互为相反数,试求代数式1/ab+1/(a+2)(b+2)+...+1/(a=2009)(b+2009)的值

已知/ab-2/与/b-1/互为相反数,试求代数式1/ab+1/(a+2)(b+2)+...+1/(a=2009)(b+2009)的值
/ab-2/与/b-1/互为相反数
ab-2=0
b-1=0
ab=2
b=1,a=2
1/ab+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)
=1/2+1/4*3+------+1/2011*2010
=1/2(1-1/2+1/2-1/3+-----+1/2010-1/2011)
=1/2(1-1/2011)
=(1/2)*(2010/2011)
=1005/2011

由ab-2=0,b-1=0
得a=2 b=1
所以原式=1/2+1/(4*3)+1/5*4+…+1/(2011*2010)=1/2+1/3-1/4+1/4-1/5+…+1/2010-1/2011=1/2-1/2011=2009/4022

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