Question

So sánh

A=100²⁰¹⁶+1/100²⁰¹⁷+1 và B=100²⁰¹⁷+1/100²⁰¹⁸+1

Answer 1

Ta có:

A=\(\frac{100^{2016}+1}{100^{2017}+1}\Rightarrow100A=\frac{100\left(100^{2016}+1\right)}{100^{2017}+1}=\frac{100^{2017}+100}{100^{2017}+1}=\frac{100^{2017}+1+99}{100^{2017}+1}=1+\frac{99}{100^{2017}+1}\)\(B=\frac{100^{2017}+1}{100^{2018}+1}\Rightarrow100B=\frac{100\left(100^{2017}+1\right)}{100^{2018}+1}=\frac{100^{2018}+100}{100^{2018}+1}=\frac{100^{2018}+1+99}{100^{2018}+1}=1+\frac{99}{100^{2018}+1}\)Ta có:

\(\frac{99}{100^{2017}+1}>\frac{99}{100^{2018}+1}\)\(\Rightarrow1+\frac{99}{100^{2017}+1}>1+\frac{99}{100^{2018}+1}\)

\(\Rightarrow100A>100B\Rightarrow A>B\)