Question

So sanh: 2011/2013+2013/2015+2015/2017+2017/2011 va 4

Answer 1

2011/2013+2013/2015+2015/2017+2017/2011   >    4

Answer 2

Ta có:

 \(\frac{2011}{2013}+\frac{2013}{2015}+\frac{2015}{2017}+\frac{2017}{2011}\)và 4

=\(\frac{2011}{2011}\)(Triệt tiêu 2013;2015;2017 vì đều có ở mẫu và tử)và4

=1 và 4

=1<4;\(\frac{1}{4}\)

Suy ra :

Answer 3

2011/2013+2013/2015+2015/2017+2017/2011 = 4,000005921 (bấm máy tính)

=> 2011/2013+2013/2015+2015/2017+2017/2011 > 4

Answer 4

Ta có: 

   2011/2013+2013/2015+2015/2017+2017/2011=2011/2011=1

  Do 1<4

=>2011/2013+2013/2015+2015/2017+2017/2011<4

Answer 5

là dấu > ha chị Nguyễn Trần Minh Thư

Answer 6

\(\frac{2011}{2013}+\frac{2013}{2015}+\frac{2015}{2017}+\frac{2017}{2011}\)

\(=\left(1-\frac{2}{2013}\right)+\left(1-\frac{2}{2015}\right)+\left(1-\frac{2}{2017}\right)+\left(1+\frac{6}{2011}\right)\)

\(=1-\frac{2}{2013}+1-\frac{2}{2015}+1-\frac{2}{2017}+1+\frac{6}{2011}\)

\(=\left(1+1+1+1\right)-\left(\frac{2}{2013}+\frac{2}{2015}+\frac{2}{2017}-\frac{6}{2011}\right)\)

Vì  \(\frac{2}{2013}+\frac{2}{2015}+\frac{2}{2017}<\frac{6}{2011}\)

\(\Rightarrow\frac{2}{2013}+\frac{2}{2015}+\frac{2}{2017}-\frac{6}{2011}\) là 1 số âm

Mà ( + ) - ( - ) ra ( + )

Nên 4 +  \(\left(\frac{2}{2013}+\frac{2}{2015}+\frac{2}{2017}-\frac{6}{2011}\right)\) > 4

Hay \(\frac{2011}{2013}+\frac{2013}{2015}+\frac{2015}{2017}+\frac{2017}{2011}>4\)

Vậy  \(\frac{2011}{2013}+\frac{2013}{2015}+\frac{2015}{2017}+\frac{2017}{2011}>4\)