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\(10A=\frac{10^{2015}+1+9}{10^{2015}+1}=1+\frac{9}{10^{2015}+1}\)
\(10B=\frac{10^{2017}+1+9}{10^{2017}+1}=1+\frac{9}{10^{2017}+1}\)
Vì \(\frac{9}{10^{2015}+1}>\frac{9}{10^{2017}+1}\Rightarrow10A>10B\Rightarrow A>B\)
Vì 20162016 + 1 < 20162017 + 1
\(\Rightarrow\frac{2016^{2016}+1}{2016^{2017}+1}< \frac{2016^{2016}+1+2015}{2016^{2016}+1+2015}=\frac{2016^{2016}+2016}{2016^{2017}+2016}=\frac{2016\left(2016^{2015}+1\right)}{2016\left(2016^{2016}+1\right)}\)
\(=\frac{2016^{2015}+1}{2016^{2016}+1}=B\)
\(\Rightarrow\)A < B
Ta có :
\(A=\frac{2016^{2016}+1}{2016^{2017}+1}< \frac{2016^{2016}+2015+1}{2016^{2017}+2015+1}=\frac{2016^{2016}+2016}{2016^{2017}+2016}=\frac{2016.\left(2016^{2015}+1\right)}{2016.\left(2016^{2016}+1\right)}\)
\(=\frac{2016^{2015}+1}{2016^{2016}+1}=B\)
\(\Rightarrow A< B\)
Ta có :
\(\frac{2015}{2016}>\frac{2015}{2016+2017}\)
\(\frac{2016}{2017}>\frac{2016}{2016+2017}\)
\(\Rightarrow\frac{2015}{2016}+\frac{2016}{2017}>\frac{2015+2016}{2016+2017}\)
\(\Rightarrow A>\frac{2015+2016}{2016+2017}\)
\(\Rightarrow A>B\)
Chúc bạn học tốt !!!
\(A=\frac{2015}{2016}+\frac{2016}{2017}\) \(B=\frac{2015+2016}{4033}\)
\(A=\frac{2015}{2016}+\frac{2016}{2017}\) \(B=\frac{2015}{4033}+\frac{2016}{4033}\)
\(\Rightarrow A>B\)