1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2012)(b+2012),ab=2,b=1错了,是1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2011)(b+2011)+1/(a+2012)(b+2012),ab=2,b=1

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1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2012)(b+2012),ab=2,b=1错了,是1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...

1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2012)(b+2012),ab=2,b=1错了,是1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2011)(b+2011)+1/(a+2012)(b+2012),ab=2,b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2012)(b+2012),ab=2,b=1
错了,是1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2011)(b+2011)+1/(a+2012)(b+2012),ab=2,b=1

1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2012)(b+2012),ab=2,b=1错了,是1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2011)(b+2011)+1/(a+2012)(b+2012),ab=2,b=1
解由ab=2,b=1
知a=2
故1/ab=1/1*2=1/1-1/2
1/(a+1)(b+1)=1/2*3=1/2-1/3
1/(a+2)(b+2)=1/3*4=1/3-1/4
.
1/(a+2012)(b+2012)=1/2013*2014=1/2013-1/2014
上述各式相加得
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2012)(b+2012)
=1/1-1/2+1/2-1/3+1/3-1/4+.+1/2013-1/2014
=1/1-1/2014
=2013/2014