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Ta có: \(\frac{1}{2}A=\frac{2^{2018}-3}{2^{2017}-1}.\frac{1}{2}=\frac{2^{2018}-3}{2^{2018}-2}=\frac{2^{2018}-2-1}{2^{2018}-2}=1-\frac{1}{2^{2018}-2}\)
Tương tự ta có: \(\frac{1}{2}B=1-\frac{1}{2^{2017}-2}\)
Vì \(2^{2018}>2^{2017}\)\(\Rightarrow2^{2018}-2>2^{2017}-2\)
\(\Rightarrow\frac{1}{2^{2018}-2}< \frac{1}{2^{2017}-2}\)\(\Rightarrow1-\frac{1}{2^{2018}-2}>1-\frac{1}{2^{2017}-2}\)
hay \(\frac{1}{2}A>\frac{1}{2}B\)\(\Rightarrow A>B\)( vì \(\frac{1}{2}>0\))
Vậy \(A>B\)
a: \(0.2=\dfrac{2}{10}\)
10>7
=>\(\dfrac{2}{10}< \dfrac{2}{7}\)
=>\(\dfrac{2}{7}>0.2\)
b: \(-\dfrac{1^5}{6}=\dfrac{-1}{6}=\dfrac{-3}{18}\)
\(\dfrac{8}{-9}=-\dfrac{16}{18}\)
mà -3>-16
nên \(-\dfrac{1^5}{6}>\dfrac{8}{-9}\)
c: \(\dfrac{2017}{2016}>1\)
\(1>\dfrac{2017}{2018}\)
Do đó: \(\dfrac{2017}{2016}>\dfrac{2017}{2018}\)
d: \(-\dfrac{249}{333}=\dfrac{-249:3}{333:3}=\dfrac{-83}{111}\)
e: \(\dfrac{5^1}{3}=\dfrac{5}{3}=\dfrac{15}{9}\)
\(\dfrac{4^8}{9}=\dfrac{65536}{9}\)
mà 15<65536
nên \(\dfrac{5^1}{3}< \dfrac{4^8}{9}\)
f: 13,589<13,612
\(\frac{B}{A}=\frac{\frac{2^{2017}-3}{2^{2016}-1}}{\frac{2^{2018}-3}{2^{2017}-1}}=\frac{2^{2017}-3}{2^{2016}-1}\cdot\frac{2^{2017}-1}{2^{2018}-3}\)
\(=\frac{2^{4034}-4.2^{2017}+3}{2^{4034}-3.2^{2016}-2^{2018}+3}\)
Ta có: 4.22017 = 22019
3.22016 + 22018 < 4.22016 + 22018 = 2.22018 = 22019
=> 4.22017 > 3.22016 + 22018
=> - 4.22017 < - 3.22016 - 22018
\(\Rightarrow\frac{2^{4034}-4.2^{2017}+3}{2^{4034}-3.2^{2016}-2^{2018}+3}< 1\)
=> B < A
1: so sánh 2016/2017+2017/2018
vì 2016/2017 > 1/2017 >1/2018 =
> 2016/2017+2017/2018 >1/2018+2017/2018=1
vậy .....
a) ta có: \(1-\frac{2016}{2017}=\frac{1}{2017}\)
\(1-\frac{2017}{2018}=\frac{1}{2018}\)
\(\Rightarrow\frac{1}{2017}>\frac{1}{2018}\Rightarrow1-\frac{2016}{2017}>1-\frac{2017}{2018}\Rightarrow\frac{2016}{2017}< \frac{2017}{2018}\)
b) ta có: \(\frac{2017}{2016}-1=\frac{1}{2016};\frac{2018}{2017}-1=\frac{1}{2017}\)
\(\Rightarrow\frac{1}{2016}>\frac{1}{2017}\Rightarrow\frac{2017}{2016}-1>\frac{2018}{2017}-1\Rightarrow\frac{2017}{2016}>\frac{2018}{2017}\)
a: Ta có: \(A=2018^2-2017^2=2018+2017\)
\(B=2017^2-2016^2=2017+2016\)
mà 2018>2016
nên A>B
giúp mk câu b nx đc ko