Question

So sánh 2 p/số

\(A=\dfrac{2014^{2013}+1}{2014^{2014}+1};B=\dfrac{2014^{2012}+1}{2014^{2013}+1}\)

Answer 1

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Giups em vs

Answer 2

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Answer 3

A=\(\dfrac{2014^{2013}+1}{2014^{2014}+1}\)<\(\dfrac{2014^{2013}+1+2013}{2014^{2014}+1+2013}\)

=\(\dfrac{2014^{2013}+2014}{2014^{2014}+2014}\)=\(\dfrac{2014\left(2014^{2012}+1\right)}{2014\left(2014^{2013}+1\right)}\)

=\(\dfrac{2014^{2012}+1}{2014^{2013}+1}\)=B

Vậy A<B

Answer 4

Ta có :

\(2014A=\dfrac{2014^{2014}+2014}{2014^{2014}+1}=\dfrac{2014^{2014}+1+2013}{2014^{2014}+1}\)\(=1+\dfrac{2013}{2014^{2014}+1}\)\(\left(1\right)\)

\(2014B=\dfrac{2014^{2013}+2014}{2014^{2013}+1}=\dfrac{2014^{2013}+1+2013}{2014^{2013}+1}=1+\dfrac{2013}{2014^{2013}+1}\)\(\left(2\right)\)

Vì \(1+\dfrac{2013}{2014^{2014}+1}< \dfrac{2013}{2014^{2013}+1}\)\(\left(3\right)\)

Từ \(\left(1\right)+\left(2\right)+\left(3\right)\Rightarrow2014A< 2014B\)

\(\Rightarrow A< B\)

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