Question

[Ơ Ơ BUỒN CƯỜI]

So sánh : M = 2009^2009 + 1 / 2009^2010 + 1 và N = 2009^2010 - 2 / 2009^2011 - 2

Answer 1

[Thanh Tùng DZ]

Ta có :

\(N=\frac{2009^{2010}-2}{2009^{2011}-2}< \frac{2009^{2010}-2+2011}{2009^{2011}-2+2011}\)

\(=\frac{2009^{2010}+2009}{2009^{2011}+2009}=\frac{2009.\left(2009^{2009}+1\right)}{2009.\left(2009^{2010}+1\right)}\)

\(=\frac{2009^{2009}+1}{2009^{2010}+1}=M\)

Vậy \(M>N\)

Answer 2

[ST]

Ta có: \(B< 1\)

\(\Rightarrow B< \frac{2009^{2010}-2+3}{2009^{2011}-2+3}=\frac{2009^{2010}+1}{2009^{2011}+1}\left(1\right)\)

Mà \(\frac{2009^{2010}+1}{2009^{2011}+1}< 1\)

\(\Rightarrow\frac{2009^{2010}+1}{2009^{2011}+1}< \frac{2009^{2010}+1+2008}{2009^{2011}+1+2008}=\frac{2009^{2010}+2009}{2009^{2011}+2009}=\frac{2009\left(2009^{2009}+1\right)}{2009\left(2009^{2010}+1\right)}=\frac{2009^{2009}+1}{2009^{2010}+1}=A\left(2\right)\)

Từ (1) và (2) suy ra A > B