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

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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计算1/ab+1/(a+2)(b+2)+1/(a+4

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
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

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
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)
=1007/4032