已知b-1的相反数等于他本身,ab与-2互为相反数求1/ab+1/(a+1)(b+1)+.+1(2009+a)(2009+b)的值

因为b-1的相反数是它本身，也就是b-1=-(b-1) 得出b=1
ab与-2互为相反数，那么ab=2 得出a=2
那么下面的式子就是1/2+1/(2×3)+1/(3×4).....................+1/(2010)(2011)
=1-1/2+1/2-1/3+..............................1/2010-1/2011
=1-1/2011
=2010/2011

b=1，a=2
1/ab+1/(a+1)(b+1)+......+1(2009+a)(2009+b)
=1/(1*2)+1/(2*3)+....+1/(2010*2011)
=1-1/2+1/2-1/3+...+1/2010-1/2011
=1-1/2011
=2010/2011

b-1=1-b
b=1
ab-2=0
a=2
1/ab+1/(a+1)(b+1)+.+1(2009+a)(2009+b)
=1/1x2+1/2x3+1/3x4+...+1/2010x2011
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2010-1/2011)
=1-1/2011
=2010/2011