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\(A=\frac{2018^{2019}+1}{2018^{2019}-2017}=\frac{2018^{2019}-2017+2018}{2018^{2019}-2017}=\frac{2018^{2019}-2017}{2018^{2019}-2017}+\frac{2018}{2018^{2019}-2017}=1+\frac{2018}{2018^{2019}-2017}\)\(B=\frac{2018^{2019}+2}{2018^{2019}-2016}=\frac{2018^{2019}-2016+2018}{2018^{2019}-2016}=\frac{2018^{2019}-2016}{2018^{2019}-2016}+\frac{2018}{2018^{2019}-2016}=1+\frac{2018}{2018^{2019}-2016}\)Ta có: \(2018^{2019}-2017< 2018^{2019}-2016\)
\(\Rightarrow\frac{2018}{2018^{2019}-2017}>\frac{2018}{2018^{2019}-2016}\)
\(\Rightarrow1+\frac{2018}{2018^{2019}-2017}>1+\frac{2018}{2018^{2019}-2016}\)
\(\Rightarrow A>B\)
Vậy...
Ta có :
\(A=\frac{2018^{2019}+1}{2018^{2019}-2017}=\frac{2018^{2019}-2017+2018}{2018^{2019}-2017}=1+\frac{2018}{2018^{2019}-2017}\)
\(B=\frac{2018^{2019}+2}{2018^{2019}-2016}=\frac{2018^{2019}-2016+2018}{2018^{2019}-2016}=1+\frac{2018}{2018^{2019}-2016}\)
Vì \(2018^{2019}-2017< 2018^{2019}-2016\)nên \(\frac{2018}{2018^{2019}-2017}>\frac{2018}{2018^{2019}-2016}\)hay \(A>B\)
~ Hok tốt ~
A = 20 + 21 + 22 + ... + 22017
2A = 21 + 22 + 23 + ... + 22018
2A - A = A = 22018 - 1
\(\Rightarrow\)A = B = 22018 - 1
Ta có: A = 20+21+22+23+.....+22018
\(\Rightarrow\)2A= 21+22+23+24+.....+22019
Do đó: 2A - A = (21+22+23+24+.....+22019) - (20+21+22+23+......+22018)
\(\Rightarrow\) A = 22019 - 1
Vì vậy, A=B
Vì \(2^{2018}+2^{2017}>2^{2019}\)
nên \(2^{2018}+2^{2017}+...+2^2+2^1>2^{2019}\)
nên \(2^{2019}-\left(2^{2018}+2^{2017}+...+2^2+2^1\right)=\) số âm
mà số âm < 1
⇒\(2^{2019}-\left(2^{2018}+2^{2017}+...+2^2+2^1\right)\)< 1