已知lab+2l+la+1l+0,则代数式1/(a-1)(b+1) +1/(a-2)(b+2)+^+1/(a-2009)(b+2009)
问题描述:
已知lab+2l+la+1l+0,则代数式1/(a-1)(b+1) +1/(a-2)(b+2)+^+1/(a-2009)(b+2009)
答
a=-1,b=2 ,1/(a-1)(b+1) +1/(a-2)(b+2)+^+1/(a-2009)(b+2009)=-(1/2-1/3)-(1/3-1/4)--^--(1/3000-1/3001)=--(1/2--1/3+1/3--1/4+^+1/3000-1/3001)=--(1/2--1/3001)=--2009/6002