比较(1/2+1/3+...+1/2008)(1+1/2+1/3+...+1/2007)与(1+1/2+1/3+...+1/2008)(1/2+1/3+...+1/2007)的大小
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![比较(1/2+1/3+...+1/2008)(1+1/2+1/3+...+1/2007)与(1+1/2+1/3+...+1/2008)(1/2+1/3+...+1/2007)的大小](/uploads/image/z/2715972-60-2.jpg?t=%E6%AF%94%E8%BE%83%281%2F2%2B1%2F3%2B...%2B1%2F2008%29%281%2B1%2F2%2B1%2F3%2B...%2B1%2F2007%29%E4%B8%8E%281%2B1%2F2%2B1%2F3%2B...%2B1%2F2008%29%281%2F2%2B1%2F3%2B...%2B1%2F2007%29%E7%9A%84%E5%A4%A7%E5%B0%8F)
比较(1/2+1/3+...+1/2008)(1+1/2+1/3+...+1/2007)与(1+1/2+1/3+...+1/2008)(1/2+1/3+...+1/2007)的大小
比较(1/2+1/3+...+1/2008)(1+1/2+1/3+...+1/2007)与(1+1/2+1/3+...+1/2008)(1/2+1/3+...+1/2007)的大小
比较(1/2+1/3+...+1/2008)(1+1/2+1/3+...+1/2007)与(1+1/2+1/3+...+1/2008)(1/2+1/3+...+1/2007)的大小
设(1/2+1/3+...+1/2008)=a (1/2+1/3+...+1/2007)=b
(1/2+1/3+...+1/2008)(1+1/2+1/3+...+1/2007)=a(1+b)
(1+1/2+1/3+...+1/2008)(1/2+1/3+...+1/2007)=b(1+a)
a(1+b)-b(1+a)=a+ab-b+ab
=a-b
a>b
(1/2+1/3+...+1/2008)(1+1/2+1/3+...+1/2007)>(1+1/2+1/3+...+1/2008)(1/2+1/3+...+1/2007)
解设:x=1/2+1/3+...+1/2007+1/2008
y=1/2+1/3+...+1/2007
(1/2+1/3+...+1/2008)(1+1/2+1/3+...+1/2007)=x(1+y)
(1+1/2+1/3+...+1/2008)(1/2+1/3+...+1/2007)=y(1+x)
则有:x(1+y)-y(1+x)=x + xy...
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解设:x=1/2+1/3+...+1/2007+1/2008
y=1/2+1/3+...+1/2007
(1/2+1/3+...+1/2008)(1+1/2+1/3+...+1/2007)=x(1+y)
(1+1/2+1/3+...+1/2008)(1/2+1/3+...+1/2007)=y(1+x)
则有:x(1+y)-y(1+x)=x + xy - y - xy
=x - y
=1/2008 > 0
所以 (1/2+1/3+...+1/2008)(1+1/2+1/3+...+1/2007)>(1+1/2+1/3+...+1/2008)(1/2+1/3+...+1/2007)
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