ta thấy:
\(\frac{1}{\sqrt{1}}>\frac{1}{10}\)
\(\frac{1}{\sqrt{2}}>\frac{1}{10}\)
....
\(\frac{1}{\sqrt{100}}=\frac{1}{10}\)
=> \(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{100}}>\frac{1}{10}+\frac{1}{10}+...+\frac{1}{10}=\frac{1}{10}.100=10\)
=> \(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{100}}>10\) (đpcm)