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
问题描述:
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
答
丨ab-2丨加丨1-b丨=0则,ab=2,b=1所以,a=2,b=11/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...