已知ab是有理数,满足(a-1)+丨ab-2丨=0,...已知ab是有理数,且满足丨a-1丨+丨ab-2丨=0,求ab分之1+ (a+1)(b+1)分之1+(a+2)(b+2)分之1+····+(a+2012)(b+2012)分之1的值.

问题描述:

已知ab是有理数,满足(a-1)+丨ab-2丨=0,...
已知ab是有理数,且满足丨a-1丨+丨ab-2丨=0,求ab分之1+ (a+1)(b+1)分之1+(a+2)(b+2)分之1+····+(a+2012)(b+2012)分之1的值.

丨a-1丨+丨ab-2丨=0
所以a-1=0
ab-2=0
则a=1
b=2/a=2
所以原式=1/1×2+1/2×3+……+1/2013×2014
=1-1/2+1/2-1/3+……+1/2013-1/2014
=1-1/2014
=2013/2014