Question

So sánh A và B:

A=\(\dfrac{9}{a^{2013}}\)+\(\dfrac{7}{a^{2014}}\) và B=\(\dfrac{8}{a^{2014}}\)+\(\dfrac{8}{a^{2013}}\) (với a thuộc N*)

Answer 1

Ta có:

\(A=\dfrac{9}{a^{2013}}+\dfrac{7}{a^{2014}}\)

\(=\left(\dfrac{8}{a^{2013}}+\dfrac{1}{a^{2013}}\right)+\left(\dfrac{8}{a^{2014}}-\dfrac{1}{a^{2014}}\right)\)

\(=\left(\dfrac{8}{a^{2013}}+\dfrac{8}{a^{2014}}\right)+\left(\dfrac{1}{a^{2013}}-\dfrac{1}{a^{2014}}\right)\)

\(B=\dfrac{8}{a^{2014}}+\dfrac{8}{a^{2013}}\)

\(=\dfrac{8}{a^{2013}}+\dfrac{8}{a^{2014}}\)

Vì \(\dfrac{1}{a^{2013}}>\dfrac{1}{a^{2014}}\Rightarrow\dfrac{1}{a^{2013}}-\dfrac{1}{a^{2014}}>0\)

\(\Rightarrow\left(\dfrac{8}{a^{2013}}+\dfrac{8}{a^{2014}}\right)+\left(\dfrac{1}{a^{2013}}-\dfrac{1}{a^{2014}}\right)>\dfrac{8}{a^{2013}}+\dfrac{8}{a^{2014}}\)

Vậy \(A>B\)