Question

-丨+2丨相反数

已知丨ab-6丨与丨b-2丨互为相反数
(1)求 a 与b 值.
(2)1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2009)(b+2009)的值.

Answer 1

(1)∵丨ab-6丨与丨b-2丨都是非负的,
又它们互为相反数
∴丨ab-6丨=丨b-2丨=0
b=2,a=3
(2) 1/(2*3) = 1/2 -1/3
1/(3*4) = 1/3 - 1/4
1/(4*5) =1/4 - 1/5
……
1/(2011*2012) =1/2011 -1/2012
∴原式= 1/2 - 1/2012 = 1005/2012