Question

So sánh:

A = \(\frac{2011^{2012}+1}{2011^{2013}+1}\)với B = \(\frac{2011^{2013}+1}{2011^{2014}+1}\)

Answer 1

Sửa lại:

Ta có:

\(2011A=\frac{2011^{2013}+2011}{2011^{2013}+1}=1+\frac{2010}{2011^{2013}+1}\)

\(2011B=\frac{2011^{2014}+2011}{2011^{2014}+1}=1+\frac{2010}{2011^{2014}+1}\)

Vì \(1+\frac{2010}{2011^{2013}+1}>1+\frac{2010}{2011^{2014}+1}\) nên 2011A > 2011 B

Từ đó A > B

Vậy A > B

Answer 2

Có:

\(2009A=\frac{2011^{2013}+2011}{2011^{2013}+1}=1+\frac{2010}{2011^{2013}+1}\)

\(2011B=\frac{2011^{2014}+2011}{2011^{2014}+1}=1+\frac{2010}{2011^{2014}+1}\)

Mà \(1+\frac{2010}{2011^{2013}+1}>1+\frac{2010}{2011^{2014}+1}\)

\(\Rightarrow2009A>2009B\)

\(\Rightarrow A>B\)

Vậy A > B