已知a与-1的差为2,b是-2的相反数,试求代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2010)(b+2010)值

a与-1的差为2a-(-1)=2a=1b是-2的相反数b+(-2)=0b=21/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2010)(b+2010)=1/1*2+1/2*3+1/3*4+1/4*5+.+1/2011*2012=1-1/2+1/2-1/3+1/3-1/4+.+1/2011-1/2012=1-1/2012=2011/2012...