Question

Cho B = \(\frac{2016^{100}+1}{2016^{90}+1}\)và C = \(\frac{2016^{99}+1}{2016^{89}+1}\)

Hãy so sánh.

Answer 1

Easy.

Ta có: Nếu \(\frac{a}{b}>1\)thì \(\frac{a}{b}>\frac{a+m}{b+m}\left(m>0\right)\)   (bạn tự c/m)

Mặt khác,ta có: \(C=\frac{2016^{99}+1}{2016^{89}+1}=\frac{2016\left(2016^{99}+1\right)}{2016\left(2016^{89}+1\right)}\)

\(=\frac{2016^{100}+2016}{2016^{90}+2016}=\frac{\left(2016^{100}+1\right)+2015}{\left(2016^{90}+1\right)+2015}\)

Mà \(\frac{\left(2016^{100}+1\right)+2015}{\left(2016^{90}+1\right)+2015}>1\)

Nên \(C=\frac{\left(2016^{100}+1\right)+2015}{\left(2016^{90}+1\right)+2015}< \frac{2016^{100}+1}{2016^{90}+1}=B\)

Vậy \(B>C\)

Answer 2

bằng nhau

Answer 3

bằng nhau