Ta có :
\(\frac{1}{\sqrt{1}}>\frac{1}{10}\)
\(\frac{1}{\sqrt{2}}>\frac{1}{10}\)
.....
\(\frac{1}{\sqrt{99}}>\frac{1}{10}\)
\(\frac{1}{\sqrt{100}}=\frac{1}{10}\)
Cộng vế theo vế ta có :\(\frac{1}{\sqrt{1}}\frac{1}{\sqrt{2}}+......+\frac{1}{\sqrt{99}}+\frac{1}{100}>100.\frac{1}{10}=10\)