Chứng minh: 1 + 1/2 + 1/3 + + 1/64 > 4
Chứng minh: \(1 + \frac{1}{2} + \frac{1}{3} + ..... + \frac{1}{{64}}\) > 4.
\(1 + \frac{1}{2} + \frac{1}{3} + ..... + \frac{1}{{64}}\)
\( = 1 + \frac{1}{2} + \left( {\frac{1}{3} + \frac{1}{4}} \right) + \left( {\frac{1}{5} + \frac{1}{6} + \frac{1}{7} + \frac{1}{8}} \right) + ... + \left( {\frac{1}{{33}} + \frac{1}{{34}} + ... + \frac{1}{{64}}} \right)\)
\( > 1 + \frac{1}{2} + 2.\frac{1}{4} + 4,\frac{1}{8} + ..... + 32.\frac{1}{{64}} = 1 + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = 4\)
Vậy \(1 + \frac{1}{2} + \frac{1}{3} + ..... + \frac{1}{{64}}\) > 4.