Question

So sánh :

A = \(\dfrac{2006}{2007}\) - \(\dfrac{2007}{2008}\) + \(\dfrac{2008}{2009}\) - \(\dfrac{2009}{2010}\)

B = \(-\dfrac{1}{2006.2007}\) - \(\dfrac{1}{2008.2009}\)

help me ~ mai mik nộp rồi

Answer 1

Khó quá bạn ơi !!!

Đợi mk nghĩ chút nha.

hjhj

Answer 2

\(A=\dfrac{2006}{2007}-\dfrac{2007}{2008}+\dfrac{2008}{2009}-\dfrac{2009}{2010}\)

\(A=\left(1-\dfrac{1}{2007}\right)-\left(1-\dfrac{1}{2008}\right)+\left(1-\dfrac{1}{2009}\right)-\left(1-\dfrac{1}{2010}\right)\)

\(A=1-\dfrac{1}{2007}-1+\dfrac{1}{2008}+1-\dfrac{1}{2009}-1+\dfrac{1}{2010}\)

\(A=\left(1-1\right)+\left(1-1\right)-\dfrac{1}{2007}+\dfrac{1}{2008}-\dfrac{1}{2009}+\dfrac{1}{2010}\)

\(A=\dfrac{1}{2007}+\dfrac{1}{2008}-\dfrac{1}{2009}+\dfrac{1}{2010}\)

\(B=-\dfrac{1}{2006.2007}-\dfrac{1}{2008.2009}\)

\(B=-\left(\dfrac{1}{2006}-\dfrac{1}{2007}\right)-\left(\dfrac{1}{2008}-\dfrac{1}{2009}\right)\)

\(B=-\dfrac{1}{2006}+\dfrac{1}{2007}-\dfrac{1}{2008}+\dfrac{1}{2009}\)

\(B=\dfrac{1}{2007}+\dfrac{1}{2009}-\dfrac{1}{2006}+\dfrac{1}{2008}\)

Dễ dàng thấy \(A>B\)