已知根号a-1+(ab-2)=0,求ab分之1+(a+1)(b+1)分之1+...+（a+2008)(b+2008)分之

已知根号a-1+(ab-2)=0,==> a- 1 = 0 ab - 2 = 0 ==> a = 1,b = 2 1+(a+1)(b+1)分之1+...+（a+2008)(b+2008)分之1 = 1 + 1/(1*2) + 1/(2* 3) +.+ 1/(2009 * 2010) = 1 +1 - 1/2 + 1/2 - 1/3 +...+ 1/2009 - 1/2010 = 2 - 1/2010 = 4019/2010