Đáp án + Giải thích các bước giải:
Ta có:
$S=\bigg(\dfrac{1}{21} + \dfrac{1}{22} + \dfrac{1}{23} +...+ \dfrac{1}{40}\bigg) + \bigg(\dfrac{1}{41} + \dfrac{1}{42} + \dfrac{1}{43} +...+ \dfrac{1}{80}\bigg)\\$
$\Rightarrow S > \bigg(\dfrac{1}{40} + \dfrac{1}{40} + \dfrac{1}{40} +...+ \dfrac{1}{40}\bigg) + \bigg(\dfrac{1}{80} + \dfrac{1}{80} + \dfrac{1}{80} +...+ \dfrac{1}{80}\bigg)\\$
$\Rightarrow S > \dfrac{1}{2} + \dfrac{1}{2}\\$
$\Rightarrow S > 1$ (*)
Ta lại có:
$S=\bigg(\dfrac{1}{21} + \dfrac{1}{22} + \dfrac{1}{23} +...+ \dfrac{1}{40}\bigg) + \bigg(\dfrac{1}{41} + \dfrac{1}{42} + \dfrac{1}{43} +...+ \dfrac{1}{80}\bigg)\\$
$\Rightarrow S < \bigg(\dfrac{1}{20} + \dfrac{1}{20} + \dfrac{1}{20} +...+ \dfrac{1}{20}\bigg) + \bigg(\dfrac{1}{40} + \dfrac{1}{40} + \dfrac{1}{40} +...+ \dfrac{1}{40}\bigg)\\$
$\Rightarrow S < \dfrac{20}{20} + \dfrac{40}{40}\\$
$\Rightarrow S < 2$ (**)
Từ (*) và (**) $\Rightarrow 1 < S < 2$
Vậy S không là số tự nhiên
$#Noob$ $#Shut Up$
