若|a-1|+|ab-2|=0 计算:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)~+1/(a+2012)(b+2012)的值
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若|a-1|+|ab-2|=0 计算:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)~+1/(a+2012)(b+2012)的值
若|a-1|+|ab-2|=0 计算:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)~+1/(a+2012)(b+2012)的值
若|a-1|+|ab-2|=0 计算:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)~+1/(a+2012)(b+2012)的值
|a-1|+|ab-2|=0
所以a-1=ab-2=0
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
2013/2014
因为|a-1|+|ab-2|=0
所以a-1=0,ab-2=0
所以a=1,b=2
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)~~~+1/(a+2012)(b+2012)
=1/2+1/2*3+1/3*4+1/4*5+...+1/2013*2014
=1-1/2+1/2-1/3+1/3-1/4+...+1/2013-1/2014
=1-1/2014
=2013/2014
2013/2014。
a=1,b=2,
原式=1/1*2+1/2*3+~~~+1/2013*2014;
1/1*2=1/1-1/2;
1/2*3=1/2-1/3;
……
1/2013*2014=1/2013-1/2014
所以原式=1/1-1/2+1/2-1/3+1/3-~~~-1/2014=1-1/2014=2013/2014