已知|ab-8|+|2-a|=0,求1/ab+1/(a+2)(b+2)+1/(a+4)(b+4)+.+1/(a+2012)(b+2012)
问题描述:
已知|ab-8|+|2-a|=0,求1/ab+1/(a+2)(b+2)+1/(a+4)(b+4)+.+1/(a+2012)(b+2012)
答
|ab-8|+|2-a|=0∴ab=8a=2∴b=41/ab+1/(a+2)(b+2)+1/(a+4)(b+4)+.+1/(a+2012)(b+2012)=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*(1/6-1/8)+.+1/2(1/2014-1/2016)=1/2(1/2-1/4+1/4-1/6...