Ta có :
\(\frac{1}{\sqrt{1}}>\frac{1}{10}\)
\(\frac{1}{\sqrt{2}}>\frac{1}{10}\)
\(.................\)
\(\frac{1}{\sqrt{100}}=\frac{1}{10}\)
\(\Rightarrow\)\(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{100}}>\frac{1}{10}+\frac{1}{10}+...+\frac{1}{10}=\frac{100}{10}=10\) ( đpcm )
Vậy \(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{100}}>10\)
Chúc bạn học tốt ~