Question

[Shinnôsuke]

So sánh :

A=\(\frac{2009^{2009}+1}{2009^{2010}+1}\)và B=\(\frac{2009^{2010}-2}{2009^{2011}-2}\)

Answer 1

[Đinh Đức Hùng]

Do 2009²⁰¹⁰- 2 < 2009²⁰¹¹- 2 ⇒ B < 1

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

\(=\frac{2009^{2009}+1}{2009^{2010}+1}=A\Rightarrow\)B < A