已知根号a-1+(ab-2)平方=0.求1/ab+1/(a+2)(b+2)+...+1/(a+2011)(b+2011)的值
人气:480 ℃ 时间:2019-08-20 14:13:13
解答
a-1=0ab-2=0∴a=1b=21/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+...+1/(a+2011)(b+2011)=1/1×2+1/2×3+1/3×4+……+1/2012×2013=1-1/2+1/2-1/3+1/3-1/4+1/4-1/2012+1/2012-1/2013=2012/2013
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