Question

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)+..

Answer 1

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