已知|ab-2|+|b-1|=0,试求:1/ab+1/(a+b)(b+1)+1/(a+2)(b+2)+.1/(a+2007)(b+2007)
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已知|ab-2|+|b-1|=0,试求:1/ab+1/(a+b)(b+1)+1/(a+2)(b+2)+.1/(a+2007)(b+2007)
已知|ab-2|+|b-1|=0,试求:1/ab+1/(a+b)(b+1)+1/(a+2)(b+2)+.1/(a+2007)(b+2007)
已知|ab-2|+|b-1|=0,试求:1/ab+1/(a+b)(b+1)+1/(a+2)(b+2)+.1/(a+2007)(b+2007)
|ab-2|+|b-1|=0,
|ab-2|>=0,|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+2007)(b+2007)
=1/2+1/6+1/12+.+1/2008*2009
=1-1/2+1/2-1/3+1/3-1/4+.+1/2008-1/2009
=1-1/2009
=2008/2009
|ab-2|+|b-1|=0,
|ab-2|>=0,|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+2007)(b+2007)
=1/2+1/6+1/12+.....+1/2008*2009
=1-1/2+1/2-1/3+1/3-1/4+.....+1/2008-1/2009
=1-1/2009
=2008/2009
|ab-2|+|b-1|=0,
|b-1|=0,b=1
|ab-2|=0,a=2
1/ab+1/(a+b)(b+1)+1/(a+2)(b+2)+.....1/(a+2007)(b+2007)
=1/(2*1)+1/(2+1)(1+1)+1/(2+2)(1+2)+......1/(2+2007)(1+2007)
=1/(1*2)+1/(2*3)+1/(3*4)+......1/(2008*2009)
=1-1/2+1/2-1/3+1/3-1/4+.....+1/2008-1/2009
=1-1/2009=2008/2009