so sánh A=2016/100^20+2016/100^30 và B=2017/100^20+2015/100^30

Đáp án:

 A<B

Giải thích các bước giải:

$A=\frac{2016}{100^{20}}+\frac{2016}{100^{30}}=2016\left ( \frac{1}{100^{20}}+\frac{1}{100^{30}} \right )\\
B=\frac{2017}{100^{20}}+\frac{2015}{100^{30}}\\
=\frac{2016}{100^{20}}+\frac{1}{100^{20}}+\frac{2016}{100^{30}}-\frac{1}{100^{30}}\\
=2016\left ( \frac{1}{100^{20}}+\frac{1}{100^{30}} \right )+\frac{1}{100^{20}}-\frac{1}{100^{30}}\\$

Ta có $\frac{1}{100^{20}}-\frac{1}{100^{30}} >0 \Rightarrow 2016\left ( \frac{1}{100^{20}}+\frac{1}{100^{30}} \right )<2016\left ( \frac{1}{100^{20}}+\frac{1}{100^{30}} \right )+\frac{1}{10^{20}}-\frac{1}{100^{30}}
\Rightarrow A<B$