ai k mình mình k lại

\(\text{Đặt : }A=\frac{2009^{2008}+1}{2009^{2009}+1}\Rightarrow2009A=\frac{2009^{2009}+2009}{2009^{2009}+1}=1+\frac{2008}{2009^{2009}+1}\)

\(B=\frac{2009^{2007}+1}{2009^{2008}+1}\Rightarrow2009B=\frac{2009^{2008}+2009}{2009^{2008}+1}=1+\frac{2008}{2009^{2008}+1}\)

Ta thấy: \(\frac{2008}{2009^{2009}+1}<\frac{2008}{2009^{2008}+1}\)

=>2009A<2009B =>A<B

Hay \(\frac{2009^{2008}+1}{2009^{2009}+1}<\frac{2009^{2007}+1}{2009^{2008}+1}\)

b)Đề chưa rõ xem lại

Đặt : A=20092008+120092009+1⇒2009A=20092009+200920092009+1=1+200820092009+1Đặt : A=20092008+120092009+1⇒2009A=20092009+200920092009+1=1+200820092009+1

B=20092007+120092008+1⇒2009B=20092008+200920092008+1=1+200820092008+1B=20092007+120092008+1⇒2009B=20092008+200920092008+1=1+200820092008+1

Ta thấy: 200820092009+1<200820092008+1200820092009+1<200820092008+1

=>2009A<2009B =>A<B

Hay 20092008+120092009+1<20092007+120092008+1

2009²⁰⁰⁸ +1/2009²⁰⁰⁹ +1 >....

de qua viet moi tay

Ta có : ''Phần hơn'' của \(\frac{7^{58}+2}{7^{57}+2}\) là :

             \(\frac{7^{58}+2}{^{ }7^{57}+2}\) \(-\) 1 = \(\frac{7^{57}.6}{7^{57}+2}\)

             ''Phần hơn'' của \(\frac{5^{57}+2017}{5^{56}+2017}\) với 1 là :

             \(\frac{7^{57}+2017}{7^{56}+2017}\) \(-\) 1 = \(\frac{7^{56}.6}{7^{56}+2017}\)

           Ta có :\(\frac{7^{56}.6}{7^{56}+2017}\) = \(\frac{7^{56}.7.6}{\left(7^{56}+2017\right)7}\) = \(\frac{7^{57}.6}{7^{57}+14119}\)

         Ta thấy \(\frac{7^{57}.6}{7^{57}+2}\)> \(\frac{7^{57}.6}{7^{57}+14119}\)

         Suy ra \(\frac{7^{57}.6}{7^{57}+2}\) > \(\frac{7^{56}.6}{7^{56}+2017}\)

         Do đó \(\frac{7^{58}+2}{7^{57}+2}\) > \(\frac{7^{57}+2017}{7^{56}+2017}\)

ồ thú vị đấy mình học rồi nhưng busy thông cảm ha^_^

ngoài ra a/b>1 thì a+m/b+m > 1 (m thuộc z, m khác 0) và a,b cậu biết rồi đó

\(\frac{a}{b}=\frac{ab+ac}{b\left(b+c\right)};\frac{a+c}{b+c}=\frac{ab+bc}{b\left(b+c\right)}\Rightarrow ab+bc>ab+ac\left(\frac{a}{b}< 1\right)\Rightarrow dpcm\)