1.已知1/2*3=1/2-1/3=1/6,1/3*4=1/3-1/4=1/12,...请结合下面题中给出的已知条件观察分析所求值的等式,并将其解出.如果有理数a和b满足等式|ab-2|+|1-b|=0,试求【1/ab】+【1/(a+1)(b+1)】+【1/(a+2)(b+2)】+...+【1/(a

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1.已知1/2*3=1/2-1/3=1/6,1/3*4=1/3-1/4=1/12,...请结合下面题中给出的已知条件观察分析所求值的等式,并将其解出.如果有理数a和b满足等式|ab-2|+|1-b|=0,试求【1/ab】+【1/(a+1)(b+1)】+【1/(a+2)(b+2)】+...+【1/(a

1.已知1/2*3=1/2-1/3=1/6,1/3*4=1/3-1/4=1/12,...请结合下面题中给出的已知条件观察分析所求值的等式,并将其解出.如果有理数a和b满足等式|ab-2|+|1-b|=0,试求【1/ab】+【1/(a+1)(b+1)】+【1/(a+2)(b+2)】+...+【1/(a
1.已知1/2*3=1/2-1/3=1/6,1/3*4=1/3-1/4=1/12,...请结合下面题中给出的已知条件观察分析所求值的等式,并将其解出.
如果有理数a和b满足等式|ab-2|+|1-b|=0,试求【1/ab】+【1/(a+1)(b+1)】+【1/(a+2)(b+2)】+...+【1/(a+2009)(b+2009)】的值.
注明:用了【】的符号是一个分数!

1.已知1/2*3=1/2-1/3=1/6,1/3*4=1/3-1/4=1/12,...请结合下面题中给出的已知条件观察分析所求值的等式,并将其解出.如果有理数a和b满足等式|ab-2|+|1-b|=0,试求【1/ab】+【1/(a+1)(b+1)】+【1/(a+2)(b+2)】+...+【1/(a
|ab-2|+|1-b|=0
ab-2=0,1-b=0
b=1,a=2
1/[ab]+1/[(a+1)(b+1)]+1/[(a+2)(b+2)]+…… +1/[(a+2009)(b+2009)]
=1/(2*1)+1/(3*2)+1/(4*3)+……+1/(2011*2010)
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+…… +(1/2010-1/2011)
=1/1-1/2011
=2010/2011
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