Question

So sánh

A=\(\frac{2009^{2008}+1}{2009^{2009}+1}\) và B= \(\frac{2009^{2009}+1}{2009^{2010}+1}\)

Answer 1

Ta có: \(B=\frac{2009^{2009}+1}{2009^{2010}+1}<\frac{2009^{2009}+1+2008}{2009^{2010}+1+2008}\)

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

                \(=\frac{2009.\left(2009^{2008}+1\right)}{2009.\left(2009^{2009}+1\right)}\)

                \(=\frac{2009^{2008}+1}{2009^{2009}+1}=A\)

                 => B<A

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Answer 2

Ta có: $B=\frac{2009^{2009}+1}{2009^{2010}+1}<\frac{2009^{2009}+1+2008}{2009^{2010}+1+2008}$B=20092009+120092010+1 <20092009+1+200820092010+1+2008 

               $=\frac{2009^{2009}+2009}{2009^{2010}+2009}$=20092009+200920092‍010+2009 

                $=\frac{2009.\left(2009^{2008}+1\right)}{2009.\left(2009^{2009}+1\right)}$=2009.(20092008+1)2009.(20092009+1) 

                $=\frac{2009^{2008}+1}{2009^{2009}+1}=A$=20092008+120092009+1 =A

                 => B<A

Ai k mik mik k lại. Chúc các bạn thi tốt