Question

Cho phân số :

 A = 2012 / 2013 + 2013 / 2014 + 2014 / 2015 + 2015 / 2012 . CMR : A > 4

Trình bày cụ thể hộ mình nha !

Answer 1

A= 4,00000148 nên A>4

Answer 2

A = 2013/2013 - 1/2013 + 2014/2014 -1/2014 + 2015/2015 - 1/2015 + 2012/2012 + 3/2012

A = 1 - 1/2013 + 1 - 1/2014 + 1 - 1/2015 + 1 = 1/2012 + 1/2012 + 1/2012

A = 4 + ( 1/2012 - 1/2013) + (1/2012 - 1/2014) + (1/2012 - 1/ 2015)

Vì:

1/2012 > 1/2013 => 1/2012 - 1/2013>0

1/2012 > 1/2014 => 1/2012 - 1/2014>0

1/2012 > 1/2015 => 1/2012 - 1/2015>0

=>( 1/2012 - 1/2013) + (1/2012 - 1/2014) + (1/2012 - 1/ 2015) >0. 

=>4 + ( 1/2012 - 1/2013) + (1/2012 - 1/2014) + (1/2012 - 1/ 2015) > )+ 4 = 4.