Question

[Phạm Thái An]

so sánh tổng A với 3

A= 2005/2006+2006/2007+2007/2005

giúp tui nhé tui cần

Answer 1

[Trần Nguyễn Gia Phúc]

20023

Answer 2

[Mei Shine]

Ta có: \(A=\dfrac{2005}{2006}+\dfrac{2006}{2007}+\dfrac{2007}{2005}=\dfrac{2006-1}{2006}+\dfrac{2007-1}{2007}+\dfrac{2005}{2005}+\dfrac{1}{2005}+\dfrac{1}{2005}\)\(=1+1+1+\left(\dfrac{1}{2005}-\dfrac{1}{2006}+\dfrac{1}{2005}-\dfrac{1}{2007}\right)\)

\(=3+\left(\dfrac{1}{2005}-\dfrac{1}{2006}+\dfrac{1}{2005}-\dfrac{1}{2007}\right)\)

Ta thấy: \(\dfrac{1}{2005}>\dfrac{1}{2006};\dfrac{1}{2005}>\dfrac{1}{2007}\) \(\Rightarrow\dfrac{1}{2005}-\dfrac{1}{2006}+\dfrac{1}{2005}-\dfrac{1}{2007}>0\)

\(\Rightarrow A>3\)