a)
Vì \(\frac{2009}{2010}< 1\Rightarrow\frac{2009}{2010}< \frac{2009+1}{2010+1}=\frac{2010}{2011}\)
Cần nhớ:
Nếu: \(\frac{a}{b}< 1\Rightarrow\frac{a}{b}< \frac{a+n}{b+n}\left(n\inℕ^∗\right)\)
Và tương tự: \(\frac{a}{b}>1\Rightarrow\frac{a}{b}>\frac{a+n}{b+n}\left(n\inℕ^∗\right)\)
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: \(81^{100}>64^{100}\Leftrightarrow\frac{1}{81^{100}}< \frac{1}{64^{100}}\Leftrightarrow\frac{1}{3^{400}}< \frac{1}{4^{300}}\)
c) Ta có:
\(\frac{200+201}{201+202}=\frac{401}{403}< 1\)
\(\frac{200}{201}+\frac{201}{202}=1-\frac{1}{201}+1-\frac{1}{202}=2-\left(\frac{1}{201}+\frac{1}{202}\right)>1\)
=>\(\frac{200}{201}+\frac{201}{202}>\frac{200+201}{201+202}\)
