Question

so sánh

\(\dfrac{2009}{2010}\)va\(\dfrac{2010}{2011}\)

Answer 1

Ta có :

\(1-\dfrac{2009}{2010}=\dfrac{1}{2010}\\ 1-\dfrac{2010}{2011}=\dfrac{1}{2011}\)

Mà \(\dfrac{1}{2010}>\dfrac{1}{2011}\) \(\Rightarrow\dfrac{2009}{2010}< \dfrac{2010}{201}\)

Answer 2

2009/2010>2010/2011

lấy 1 trừ cho các phân số rồi so sánh

chúc bạn học tốt!

Answer 3

ta có:

\(\dfrac{2009}{2010}=\dfrac{2009+1-1}{2010}\)

\(=\dfrac{\left(2009+1\right)-1}{2010}=1-\dfrac{1}{2010}\)

tương tự:

\(\dfrac{2010}{2011}=\dfrac{2010+1-1}{2011}=1-\dfrac{1}{2011}\)

so sánh: \(1-\dfrac{1}{2010}\)và\(1-\dfrac{1}{2011}\)

ta có: \(\dfrac{1}{2010}>\dfrac{1}{2011}\)

\(\Rightarrow1-\dfrac{1}{2010}< 1-\dfrac{1}{2011}\)

\(\Rightarrow\dfrac{2009}{2010}< \dfrac{2010}{2011}\)