Question

若/ab-2/+/b-1/=0,求1÷ab+1÷(a+1)(b+1)+1÷(a+2)(b+2)+...1÷（a+2010

Answer 1

|ab-2|+|b-1|=0

因为绝对值大于等于0,因此要等式成立,则：

ab-2=0

b-1=0

=>a=2,b=1

1/(ab）+1/(a+1)(b+1)+.+1/(a+2010)(b+2010)

=1/1*2+1/2*3+.+1/2011*2012

=1-1/2+1/2-1/3+.+1/2011-1/2012

=1-1/2012

=2011/2012