ГДЗ по математике 6 класс Мерзляк ФГОС Задание 422

\[\boxed{\mathbf{422}.}\]

\[\frac{1}{31} + \frac{1}{32} + \frac{1}{33} + \ldots + \frac{1}{39} + \frac{1}{40} > \frac{1}{4}\]

\[\frac{1}{4} = \frac{10}{40};\]

\[\frac{10}{40} = \frac{1}{40} + \frac{1}{40} + \frac{1}{40} + \ldots + \frac{1}{40};\]

\[\frac{1}{31} > \frac{1}{40};\ \frac{1}{32} > \frac{1}{40};\]

\[\ \frac{1}{33} > \frac{1}{40};\ldots;\ \frac{1}{40} = \frac{1}{40}.\]

\[\frac{1}{31} + \frac{1}{32} + \frac{1}{33} + \ldots + \frac{1}{39} + \frac{1}{40} > \frac{10}{40}\]

\[\frac{1}{31} + \frac{1}{32} + \frac{1}{33} + \ldots + \frac{1}{39} + \frac{1}{40} > \frac{1}{4}.\]

\[Что\ и\ требовалось\ доказать.\]