如果有理数a,b满足丨ab-2丨加丨1-b丨=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...
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如果有理数a,b满足丨ab-2丨加丨1-b丨=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2011)(b+2012)的值
丨ab-2丨加丨1-b丨=0
则,ab=2,b=1
所以,a=2,b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2012)(b+2012)(题目中的2011不对,是2012吧)
=1/2+1/3*2+1/4*3+...1/2014*2013
=1/2+1/2-1/3+1/3-14+...+1/2013-1/2014
=1-1/2014
=2013/2014
则,ab=2,b=1
所以,a=2,b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2012)(b+2012)(题目中的2011不对,是2012吧)
=1/2+1/3*2+1/4*3+...1/2014*2013
=1/2+1/2-1/3+1/3-14+...+1/2013-1/2014
=1-1/2014
=2013/2014
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