Question

So sánh :

A = \(\dfrac{2017^{17}+1}{2017^{16}+1}\) và B = \(\dfrac{2017^{18}+1}{2017^{17}+1}\)

Answer 1

\(B=\dfrac{2017^{18}+1}{2017^{17}+1}< \dfrac{2017^{18}+1+2016}{2017^{17}+1+2016}\)
Mà \(\dfrac{2017^{18}+1+2016}{2017^{17}+1+2016}=\dfrac{2017^{18}+2017}{2017^{17}+2017}=\dfrac{2017.\left(2017^{17}+1\right)}{2017.\left(2017^{16}+1\right)}=\dfrac{2017^{17}+1}{2017^{16}+1}=A\)
=> B < A hay :
A < B

Answer 2

A > B

Answer 3

A>B

Answer 4

Vì \(2017^{18}+1>2017^{17}+1\)

\(\Rightarrow B=\dfrac{2017^{18}+1}{2017^{17}+1}>1\)

\(\Rightarrow B=\dfrac{2017^{18}+1}{2017^{17}+1}< \dfrac{2017^{18}+1+2016}{2017^{17}+1+2016}=\dfrac{2017^{18}+2017}{2017^{17}+2017}=\dfrac{2017\cdot\left(2017^{17}+1\right)}{2017\cdot\left(2017^{16}+1\right)}=A\)

Vậy B<A hay A>B