a, \(\dfrac{2009}{2010}\) và \(\dfrac{2010}{2011}\)
Ta có:
\(2009.2011=4040099\)
\(2010.2010=4040100\)
Vì \(2009.2011< 2010.2010\)
nên \(\dfrac{2009}{2010}< \dfrac{2010}{2011}\)
b, \(\dfrac{2008}{2008.2009}\) và \(\dfrac{2009}{2009.2010}\)
Ta có:
\(\dfrac{2008}{2008.2009}=\dfrac{1}{2009};\dfrac{2009}{2009.2010}=\dfrac{1}{2010}\)
Vì \(\dfrac{1}{2009}>\dfrac{1}{2010}\) nên \(\dfrac{2008}{2008.2009}>\dfrac{2009}{2009.2010}\)
Chúc bạn học tốt!!!
a)\(\dfrac{a}{b}< 1\Leftrightarrow\dfrac{a+m}{b+m}< 1\left(m\in N\right)\)
\(\dfrac{2009}{2010}< 1\)
\(\Leftrightarrow\dfrac{2009}{2010}< \dfrac{2009+1}{2010+1}\Leftrightarrow\dfrac{2009}{2010}< \dfrac{2010}{2011}\)
b)
\(\dfrac{2008}{2008.2009}=\dfrac{1}{2009}\)
\(\dfrac{2009}{2009.2010}=\dfrac{1}{2010}\)
\(\dfrac{1}{2009}>\dfrac{1}{2010}\Leftrightarrow\dfrac{2008}{2008.2009}>\dfrac{2009}{2009.2010}\)
d)
\(\dfrac{1}{3^{400}}=\dfrac{1}{\left(3^4\right)^{100}}=\dfrac{1}{81^{100}}\)
\(\dfrac{1}{4^{300}}=\dfrac{1}{\left(4^3\right)^{100}}=\dfrac{1}{64^{100}}\)
\(81^{100}>64^{100}\Leftrightarrow\dfrac{1}{81^{100}}< \dfrac{1}{64^{100}}\)
a, Lấy 1 trừ từng phân số.
\(1-\dfrac{2009}{2010}=\dfrac{1}{2010}\)
\(1-\dfrac{2010}{2011}=\dfrac{1}{2011}\)
Vì \(\dfrac{1}{2010}>\dfrac{1}{2011}\) nên \(\dfrac{2009}{2010}< \dfrac{2010}{2011}\).
b, \(\dfrac{2008}{2008.2009}=\dfrac{1}{2009}\)
\(\dfrac{2009}{2009.2010}=\dfrac{1}{2010}\)
Vì \(\dfrac{1}{2009}>\dfrac{1}{2010}\) nên \(\dfrac{2008}{2008.2009}>\dfrac{2009}{2009.2010}\)
c, Ta có:
\(\dfrac{2016}{2017}>\dfrac{2016}{2018}\Rightarrow\dfrac{2016}{2017}+\dfrac{2017}{2018}>\dfrac{2016}{2018}+\dfrac{2017}{2018}\)
\(\Rightarrow\dfrac{2016}{2017}+\dfrac{2017}{2018}>\dfrac{2016+2017}{2018}\)
\(\dfrac{2016+2017}{2017+2018}=\dfrac{2016+2017}{4035}\)
Vì \(\dfrac{2016+2017}{2018}>\dfrac{2016+2017}{4035}\) nên \(\dfrac{2016}{2017}+\dfrac{2017}{2018}>\dfrac{2016+2017}{2017+2018}\)
d, \(\left(\dfrac{1}{3}\right)^{400}=\left(\dfrac{1}{3}\right)^{4^{100}}=\left(\dfrac{1}{81}\right)^{100}\)
\(\left(\dfrac{1}{4}\right)^{300}=\left(\dfrac{1}{4}\right)^{3^{100}}=\left(\dfrac{1}{64}\right)^{100}\)
Vì \(\left(\dfrac{1}{81}\right)^{100}< \left(\dfrac{1}{64}\right)^{100}\) nên \(\left(\dfrac{1}{3}\right)^{400}< \left(\dfrac{1}{4}\right)^{300}\)