Ta thấy :$\sqrt[]{1} < \sqrt[]{100} ⇒ \frac{1}{\sqrt[]{1} } > \frac{1}{\sqrt[]{100}}$
Tương tự :
$ \frac{1}{\sqrt[]{2}} > \frac{1}{\sqrt[]{100}}$
$....$
$ \frac{1}{\sqrt[]{100}} = \frac{1}{\sqrt[]{100}}$
Do đó :
$ \frac{1}{\sqrt[]{1}}+ \frac{1}{\sqrt[]{2}} +...+\frac{1}{\sqrt[]{100}} > \frac{1}{\sqrt[]{100}}+ \frac{1}{\sqrt[]{100}}+...+ \frac{1}{\sqrt[]{100}} = \frac{100}{10} = 10$