Question

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

CỨU EM VS MẤY ANH CHỊ

toán lớp 6 í

Answer 1

A<B

Answer 2

Ta có B=\(\frac{2009^{2010}-2}{2009^{2011}-2}\)<1

=>\(\frac{2009^{2010}-2}{2009^{2011}-2}\)<\(\frac{2009^{2010}-2+3}{2009^{2011}-2+3}\)=\(\frac{2009^{2010}+1}{2009^{2011}+1}\)(1)

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

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

Từ (1)và(2)=>B<\(\frac{2009^{2010}+1}{2009^{2011}+1}\)<A=>B<A hay A>B

 

 

Answer 3

giải ra giùm đi