Question

1/ So sánh

a/\(\frac{2009}{2010}\)và \(\frac{2010}{2011}\)                                              b/\(\frac{1}{3^{400}}\)và \(\frac{1}{4^{300}}\)

c/\(\frac{200}{201}\)+ \(\frac{201}{202}\)và \(\frac{200+201}{201+202}\)                       d/\(\frac{2008}{2008.2009}\)và \(\frac{2009}{2009.2010}\)

 

Answer 1

a, Ta có\(\)\(\frac{2009}{2010}< \frac{2009}{2011}\)

Mà \(\frac{2009}{2011}< \frac{2010}{2011}\)

Vậy\(\frac{2009}{2010}< \frac{2010}{2011}\)

Ta có :\(\frac{1}{3^{400}}=\frac{1}{\left(3^4\right)^{100}}=\frac{1}{81^{100}}\)

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

Vì\(\frac{1}{81^{100}}< \frac{1}{64^{100}}\)

Vậy\(\frac{1}{3^{400}}< \frac{1}{4^{300}}\)

c, Ta có : B=\(\frac{200+201}{201+202}=\frac{200}{201+202}+\frac{201}{201+202}\)

\(\Rightarrow\frac{200}{201}>\frac{200}{201+202}\)

\(\frac{201}{202}>\frac{201}{201+202}\)

Vậy A>B

d, Ta có \(A=\frac{2008}{2008\times2009}=\frac{1}{2019}\) 

\(B=\frac{2009}{2009\times2010}=\frac{1}{2010}\)

Vì \(\frac{1}{2009}>\frac{1}{2010}\)

Vậy A>B