Question

[Lê Thị Trà My]

so sánh

a) 

\(\frac{2009}{2010}\) và \(\frac{2010}{2011}\)

b)

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

c)

\(\frac{2008}{2008.2009}\) và \(\frac{2009}{2009.2010}\)

d)

\(\frac{200}{201}\)+\(\frac{201}{202}\) và \(\frac{200+201}{201+202}\)

Làm ơn ghi cách giải giúp mình. Mình cần cách giải

Answer 1

[BAN is VBN]

a) Ta có:

\(1-\frac{2009}{2010}=\frac{1}{2010}\)

\(1-\frac{2010}{2011}=\frac{1}{2011}\)

       Vì \(\frac{1}{2010}>\frac{1}{2011}\)=> \(\frac{2009}{2010}<\frac{2010}{2011}\)

b) 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 81¹⁰⁰ > 64¹⁰⁰ => \(\frac{1}{81^{100}}<\frac{1}{64^{100}}\)=> \(\frac{1}{3^{400}}<\frac{1}{4^{300}}\)

c) Ta có:

\(\frac{2008}{2008\cdot2009}=\frac{1}{2009}\)

\(\frac{2009}{2009\cdot2010}=\frac{1}{2010}\)

         Vì \(\frac{1}{2009}>\frac{1}{2010}\) => \(\frac{2008}{2008\cdot2009}>\frac{2009}{2009\cdot2010}\)

d) Ta có:

\(\frac{200}{201}+\frac{201}{202}=\frac{200\cdot202+201^2}{201\cdot202}>1\)

\(\frac{200+201}{201+202}=\frac{401}{403}<1\)

=> \(\frac{200\cdot202+201^2}{201\cdot202}>\frac{401}{403}\)=> \(\frac{200}{201}+\frac{201}{202}>\frac{200+201}{201+202}\)

Answer 2

[tiểu thư họ Hồ]

a)ta có:

\(1-\frac{2009}{2010}=\frac{1}{2010};1-\frac{2010}{2011}=\frac{1}{2011}\)

dự vào công thức so sánh phần bù 

vì \(\frac{1}{2010}>\frac{1}{2011}\Rightarrow\frac{2010}{2011}>\frac{2009}{2010}\)

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

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

Vì \(\frac{1}{81^{100}}<\frac{1}{64^{100}}\Rightarrow\)\(\frac{1}{3^{400}}<\frac{1}{4^{300}}\)

c)\(\frac{2008}{2008.2009}=\frac{1}{2009};\frac{2009}{2009.2010}=\frac{1}{2010}\)

vì \(\frac{1}{2009}>\frac{1}{2010}\Rightarrow\frac{2008}{2008.2009}>\frac{2009}{2009.2010}\)

d)tính tổng hai vế rồi so sánh