对于任意非零实数a、b定义运算如下：a＊b=(a-b)/ab,求2＊1+3＊2+4＊3+``````+2006＊2007的值
题目
对于任意非零实数a、b定义运算如下：a＊b=(a-b)/ab,求2＊1+3＊2+4＊3+``````+2006＊2007的值
答案
a*b=(a-b)/ab=1/b-1/a,所以2*1+3*2+4*3+…+2006*2007=1-1/2+1/2-1/3+1/3-1/4+…+1/2005-1/2006+1/2006-1/2007=1-1/2007=2006/2007
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