\[\boxed{\mathbf{321\ (322).}\mathbf{\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[\frac{1}{31} + \frac{1}{32} + \frac{1}{33} + .. + \frac{1}{39} + \frac{1}{40} > \frac{1}{4}\]
\[\frac{1}{31} > \frac{1}{40};\ \ \frac{1}{32} > \frac{1}{40};\ \ \frac{1}{33} > \frac{1}{40};\ \]
\[\frac{1}{34} > \frac{1}{40};\ \ \frac{1}{35} > \frac{1}{40};\ \]
\[\frac{1}{36} > \frac{1}{40};\ \frac{1}{37} > \frac{1}{40};\ \ \frac{1}{38} > \frac{1}{40};\ \]
\[\ \frac{1}{39} > \frac{1}{40}\]
\[\frac{1}{31} + \frac{1}{32} + \frac{1}{33} + .. + \frac{1}{39} + \frac{1}{40} >\]
\[> \frac{1}{40} + \frac{1}{40} + \frac{1}{40} + .. + \frac{1}{40} + \frac{1}{40} =\]
\[= \frac{10}{40} = \frac{1}{4} \Longrightarrow верно,\ ч.т.д.\]
\[\boxed{\mathbf{321\ (}\mathbf{с}\mathbf{).}\mathbf{\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[\frac{1}{10} + \frac{1}{11} + \frac{1}{12} + .. + \frac{1}{18} > \frac{1}{2}\]
\[\frac{1}{10} > \frac{1}{18};\ \ \frac{1}{11} > \frac{1}{18};\ \ \frac{1}{12} > \frac{1}{18};\ \]
\[\ \frac{1}{13} > \frac{1}{18};\ \frac{1}{14} > \frac{1}{18};\ \frac{1}{15} > \frac{1}{18};\ \]
\[\frac{1}{16} > \frac{1}{18};\ \ \frac{1}{17} > \frac{1}{18}\]
\[\frac{1}{1} + \frac{1}{1} + .. + \frac{1}{18} > \frac{1}{18} + \frac{1}{18} + .. + \frac{1}{18} =\]
\[= \frac{9}{18} = \frac{1}{2} \Longrightarrow верно,\ ч.\ т.д.\]