如果有理数a、b满足|ab-2|+|1-b|=0,试求1 /ab+1/a+1)(b+1)+1/(a+2)(b+2)+..
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如果有理数a、b满足|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
有理数a、b满足|ab-2|+|1-b|=0
则必有 AB-2=0 1-B=0
===>A=2,B=1
1 /ab+1/a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)
=1/(1*2)+1/(2*3)+.+1/(2010*2011)
=1-1/2+1/2-1/3+.+1/2010-1/2011
=1-1/2011=2010/2011
则必有 AB-2=0 1-B=0
===>A=2,B=1
1 /ab+1/a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)
=1/(1*2)+1/(2*3)+.+1/(2010*2011)
=1-1/2+1/2-1/3+.+1/2010-1/2011
=1-1/2011=2010/2011
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