Toán Lớp 6: cho A=2006/2007+2007/2008+2008/2006 hãy so sánh A với 3

Question

Toán Lớp 6:  cho A=2006/2007+2007/2008+2008/2006 hãy so sánh A với 3

tuanh · Answer

A=2006/2007 + 2007/2008 + 2008/2006     ={2007 -1}/2007 + {2008-1}/2008 + {2006 + 2}/2006   =2007/2007 - 1/2007 + 2008/2008 - 1/2008 + 2006/2006 + 2/2006   =1 -1/2007 + 1 - 1/2008 + 1 + 2/2006   =1 -1/2007 + 1 - 1/2008 + 1 + 1/2006 + 1/2006   =( 1 + 1 +1) + 1/2006 - 1/2007 + 1/2006 - 1/2008   =3 + 2007/2006.2007 - 2006/2006.2007 + 2008/2007.2008 - 2007/2007.2008   =3 + 1/2006.2007 + 1/2007.2008   Ta c&oacute;:   1 > 0   &rArr; 2006.2007 > 0   &rArr;1/2006.2007 > 0  (1)   1 > 0   &rArr; 2007.2008 > 0   &rArr;1/2007.2008 > 0   (2)   Từ (1) v&agrave; (2)    &rArr;1/2006.2007 + 1/2007.2008  > 0   &rArr;3 + 1/2006.2007 + 1/2007.2008  >  3   hay A > 3

maianhtuanh · Answer

2006/2007 + 2007/2008 + 2008/2009       = 1 - 1/2007 + 1 - 1/2008 + 1 - 1/2009       = ( 1 + 1 + 1 ) + ( 1/2006 - 1/2007 ) + ( 1/2006 - 1/2008 )       = 3 + ( 1/2006 - 1/2007 ) + ( 1/2006 - 1/2008 )       text{Ta thấy :}       3 = 3       1/2006 - 1/2007 > 0       1/2006 - 1/2008 > 0       => A > 3        #dtkc