Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
n < n + 1 \Rightarrow \frac{1}{n} > \frac{1}{{n + 1}}\\
A = \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + .... + \frac{1}{{31}}\\
= \left( {\frac{1}{2} + \frac{1}{3}} \right) + \left( {\frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7}} \right) + \left( {\frac{1}{8} + \frac{1}{9} + ..... + \frac{1}{{15}}} \right) + \left( {\frac{1}{{16}} + \frac{1}{{17}} + .... + \frac{1}{{31}}} \right)\\
< \left( {\frac{1}{2} + \frac{1}{2}} \right) + \left( {\frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4}} \right) + \left( {\frac{1}{8} + \frac{1}{8} + .... + \frac{1}{8}} \right) + \left( {\frac{1}{{16}} + \frac{1}{{16}} + .... + \frac{1}{{16}}} \right)\\
< 2.\frac{1}{2} + 4.\frac{1}{4} + 8.\frac{1}{8} + 16.\frac{1}{{16}}\\
= 1 + 1 + 1 + 1 = 4
\end{array}\)
