已知4a^2-4ab+2b^2-4b+4=0,试求 1/ab+1/(a+1)〈b+1〉+1/〈a+2〉(b+2〉+…+1/(a+2009)(b+2009...
问题描述：
已知4a^2-4ab+2b^2-4b+4=0,试求 1/ab+1/(a+1)〈b+1〉+1/〈a+2〉(b+2〉+…+1/(a+2009)(b+2009...
已知4a^2-4ab+2b^2-4b+4=0,试求
1/ab+1/(a+1)〈b+1〉+1/〈a+2〉(b+2〉+…+1/(a+2009)(b+2009)
请教各个老师们
答
4a^2-4ab+2b^2-4b+4=0
（2a-b）^2+(b-2)^2=0
a=1
b=2
代入1/ab+1/(a+1)〈b+1〉+1/〈a+2〉(b+2〉+…+1/(a+2009)(b+2009)
=1+1/2*3+1/3*4+…………+1/2010*2011
=1+1/2-1/3+1/3-1/4+…………1/2010-1/2011
=1-1/2011
=2010/2011