Question

So sánh A và B biết

A = \(\frac{2009}{2010}-\frac{2010}{2011}+\frac{2011}{2012}-\frac{2012}{2013}\)

B = \(-\frac{1}{2009.2010}-\frac{1}{2011.2012}\)

Answer 1

\(A=\left(1-\frac{1}{2010}\right)-\left(1-\frac{1}{2011}\right)+\left(1-\frac{1}{2012}\right)-\left(1-\frac{1}{2013}\right)=-\frac{1}{2010}+\frac{1}{2011}-\frac{1}{2012}+\frac{1}{2013}\)

\(A=-\frac{1}{2010.2011}-\frac{1}{2012.2013}\)

Vì 2010.2011 > 2009.2010 => \(\frac{1}{2010.2011}-\frac{1}{2009.2010}\)

\(-\frac{1}{2012.2013}>-\frac{1}{2011.2012}\)

=> A > B

Answer 2

alna marian: Công thức gì vậy bạn?

Answer 3

\(A=\left(1-\frac{1}{2010}\right)-\left(1-\frac{1}{2011}\right)+\left(1-\frac{1}{2012}\right)-\left(1-\frac{1}{2013}\right)\)

\(A=-\frac{1}{2010}+\frac{1}{2011}-\frac{1}{2012}+\frac{1}{2013}\)

\(A=-\frac{1}{2010.2011}-\frac{1}{2012.2013}\)

Vì \(2010.2011>2009.2010\Rightarrow\frac{1}{2010.2011}< \frac{1}{2009.2010}\Rightarrow-\frac{1}{2010.2011}>\frac{1}{2009.2010}\)

\(A=-\frac{1}{2012.2013}\)

\(B=-\frac{1}{2011.2012}\)

\(-\frac{1}{2012.2013}>-\frac{1}{2011.2012}\)

\(\Rightarrow A>B\)

Vậy \(A>B\)