Question

[Đỗ Đàm Phi Long]

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

Answer 1

[Bùi Hoàng Linh Chi]

Do 2009\(^{2010}\)-2 < 2009\(^{2011}\)-2 \(\Rightarrow\)B<1

Theo đề bài ta có: 

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