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(1/2+1/3+1/4+···+1/2007)*(1+1/2+1/3+1/4+···+1/2006)-(1+1/2+1/3+1/4+···+1/2007)*(1/2+1/3+1/4+···+1/2006)要步骤哦
题目详情
(1/2+1/3+1/4+···+1/2007)*(1+1/2+1/3+1/4+···+1/2006)-(1+1/2+1/3+1/4+···+1/2007)*(1/2+1/3+1/4+···+1/2006)要步骤哦
▼优质解答
答案和解析
答：设a=1/2+1/3+1/4+...+1/2007,b=1/2+1/3+1/4+..+1/2006
则原式化为：
(1/2+1/3+1/4+···+1/2007)*(1+1/2+1/3+1/4+···+1/2006)-(1+1/2+1/3+1/4+···+1/2007)*(1/2+1/3+1/4+···+1/2006)
=a*(1+b)-(a+1)b
=a+ab-ab-b
=a-b
=1/2007
所以：
(1/2+1/3+1/4+···+1/2007)*(1+1/2+1/3+1/4+···+1/2006)-(1+1/2+1/3+1/4+···+1/2007)*(1/2+1/3+1/4+···+1/2006)=1/2007
则原式化为：
(1/2+1/3+1/4+···+1/2007)*(1+1/2+1/3+1/4+···+1/2006)-(1+1/2+1/3+1/4+···+1/2007)*(1/2+1/3+1/4+···+1/2006)
=a*(1+b)-(a+1)b
=a+ab-ab-b
=a-b
=1/2007
所以：
(1/2+1/3+1/4+···+1/2007)*(1+1/2+1/3+1/4+···+1/2006)-(1+1/2+1/3+1/4+···+1/2007)*(1/2+1/3+1/4+···+1/2006)=1/2007
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