简单方法:因为3/4-2/3<2/3-1/2,同理可知A<B.
正常解法:
A=(1-1/2009)-(1-1/2008)=1/2008-1/2009
B=(1-1/2008)-(1-1/2007)=1/2007-1/2008
两式分别乘以2008,可知,
(1/2008-1/2009)*2008=1-2008/2009=1/2009
(1/2007-1/2008)*2008=2008/2007-1=1/2007
因为1/2009<1/2007
所以A<B.
简单方法:因为3/4-2/3<2/3-1/2,同理可知A<B.
正常解法:
A=(1-1/2009)-(1-1/2008)=1/2008-1/2009
B=(1-1/2008)-(1-1/2007)=1/2007-1/2008
两式分别乘以2008,可知,
(1/2008-1/2009)*2008=1-2008/2009=1/2009
(1/2007-1/2008)*2008=2008/2007-1=1/2007
因为1/2009<1/2007
所以A<B.