已知：字母a、b满足a-1+b-2=0．求1ab+1(a+1)(b+1)+1(a+2)(b+2)+…+1(a+2011)(b+2001)的值．

Question

已知：字母a、b满足 √(a-1)+√(b-2)=0．求(1)/(ab)+(1)/((a+1)(b+1))+(1)/((a+2)(b+2))+…+(1)/((a+2011)(b+2001))的值．

Answer 1

根据题意得：

a-1=0

b-2=0

，解得：

a=1

b=2

．
原式=(1)/(2)+(1)/(2×3)+(1)/(3×4)+…+(1)/(2012×2013)
=1-(1)/(2)+(1)/(2)-(1)/(3)+(1)/(3)-(1)/(4)+…+(1)/(2012)-(1)/(2013)
=1-(1)/(2013)
=(2012)/(2013)．