已知4a平方-4ab+2b平方-4b+4=0,求证1/ab+1/(a+1)(a+1)+...+1/(a+2009)(a+2009)的值（快点啊~）一定要准确~

题目

已知4a平方-4ab+2b平方-4b+4=0,求证1/ab+1/(a+1)(a+1)+...+1/(a+2009)(a+2009)的值（快点啊~）一定要准确~
是试求

答案

即(4a²-4ab+b²)+(b²-4b+4)=0
(2a-b)²+(b-2)²=0
所以2a-b=0,b-2=0
b=2,a=b/2=1
所以原式=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