若|1-b|+(ab-3)²=0,求1/ab+1/(a+1)(b+1)+...+1/(a+9)(b+9)

题目

若|1-b|+(ab-3)²=0,求1/ab+1/(a+1)(b+1)+...+1/(a+9)(b+9)

答案

b=1
ab=3,a=3
1/ab+1/(a+1)(b+1)+...+1/(a+9)(b+9)
=1/2(1-1/3+1/2-1/4+1/3-1/5+.+1/9-1/11+1/10-1/12)
=1/2(1+1/2-1/11-1/12)
=1/2*(132+66-12-11)/132
=175/264