以知a-1的相反数是-1,b-3的相反数是0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2006)(b+2006)的值

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以知a-1的相反数是-1,b-3的相反数是0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2006)(b+2006)的值以知a-1的相反数是-1,b-3的相反数

以知a-1的相反数是-1,b-3的相反数是0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2006)(b+2006)的值
以知a-1的相反数是-1,b-3的相反数是0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2006)(b+2006)的值

以知a-1的相反数是-1,b-3的相反数是0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2006)(b+2006)的值
(-_-!分解
a-1 = 1 =>a = 2
b-3 = 0 => b = 3
原式写成如下形式:
1/(2*3)+1/(3*4)+1/(4*5)+...+1/(2008*2009)
= 1/2-1/3+1/3-1/4+1/4-1/5+...+1/2008-1/2009
= 1/2-1/2009
= 2007/5018