Giải thích các bước giải:
$\begin{array}{l}
S = 1 + \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{4} + ... + \dfrac{1}{{32}}\\
= \left( {1 + \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{4} + \dfrac{1}{5}} \right) + \left( {\dfrac{1}{6} + \dfrac{1}{7} + ... + \dfrac{1}{{32}}} \right)\\
= \left( {\dfrac{{60 + 30 + 20 + 15 + 12}}{{60}}} \right) + \left( {\dfrac{1}{6} + \dfrac{1}{7} + ... + \dfrac{1}{{32}}} \right)\\
= \dfrac{{137}}{{60}} + \left( {\dfrac{1}{6} + \dfrac{1}{7} + ... + \dfrac{1}{{32}}} \right)\\
> \dfrac{{137}}{{60}} + \left( {\dfrac{1}{{32}} + \dfrac{1}{{32}} + ... + \dfrac{1}{{32}}} \right)\left( {Do:\dfrac{1}{6} > \dfrac{1}{{32}};\dfrac{1}{7} > \dfrac{1}{{32}}...} \right)\\
= \dfrac{{137}}{{60}} + \dfrac{{27}}{{32}}\\
= \dfrac{{1501}}{{480}}\\
> \dfrac{{1440}}{{480}} = 3\\
\Rightarrow S > 3
\end{array}$
