Question

[Nguyễn Hoàng]

AI GIÚP EM VỚI!....

so sánh

a) 2009/2010 và 2010/2011

b) 2008/2008.2009 và 2009/2009.2010

c) 2016/2017 +2017/2018 và 2016+2017/2016+2017

d) 1/3^400 và 1/4^300

kí hiệu : . = dấu nhân

^ = mũ

Answer 1

[Đức Hiếu]

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!!!

Answer 2

[Mashiro Shiina]

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)

\(\dfrac{1}{3^{400}}=\dfrac{1}{\left(3^4\right)^{100}}=\dfrac{1}{81^{100}}\)

\(\dfrac{1}{4^{300}}=\dfrac{1}{\left(4^3\right)^{100}}=\dfrac{1}{64^{100}}\)

\(81^{100}>64^{100}\Leftrightarrow\dfrac{1}{81^{100}}< \dfrac{1}{64^{100}}\)