Question

已知|ab-2|与|b-1|互为相反数，请求代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+1999)(b+1999)的值

Answer 1

互为相反数则|ab-2|+|b-1|=0
所以ab-2=0,b-1=0
b=1,a=2/b=2
所以原式=1/1*2+1/2*3+……+1/2000*2001
=1-1/2+1/2-1/3+……+1/2000-1/2001
=1-1/2001
=2000/2001

追问

请问" * " 代表的是什么

追答

乘

Answer 2

互为相反数，只能|ab-2|=0,|b-1|=0,∴a=2,b=1.
∴代数式=(1/1*2)+(1/2*3)+(1/3*4)...........(1/2000*2001)
=1-1/2+1/2-1/3+1/3-1/4+1/4-.....................+1/2000-1/2001
=1-1/2001
=2000/2001