计算1/ab+1/(a+2)(b+2)+1/(a+4)(b+4)+.1/(a+2012)(b+2012),其中a,b满足|ab-8|+|2-a|=0
问题描述:
计算1/ab+1/(a+2)(b+2)+1/(a+4)(b+4)+.1/(a+2012)(b+2012),其中a,b满足|ab-8|+|2-a|=0
答
ab-8=0 2-a=0 得 a=2 b=4原式=1/(2*4)+1/(4*6)+1/(6*8)+...+1/(2014*2016)=1/2*(1/2-1/4)+1/2*(1/4-1/6)+...+1/2*(1/2014-1/2016)=1/2*[1/2-1/4+1/4-1/6+...+1/2014-1/2016]=1/2*[1/2-1/2016]=(1008-1)/(2*2016)=100...