Răspuns:
Explicație pas cu pas:
[tex]\dfrac{1}{30}<\dfrac{1}{21}\\\\\dfrac{1}{30}<\dfrac{1}{22}\\\\~~~~~~\vdots\\\dfrac{1}{30}\leq\dfrac{1}{30}\\\\\underbrace{\dfrac{1}{30}+\dfrac{1}{30}+\ldots+\dfrac{1}{30}}<\dfrac{1}{21}+\dfrac{1}{22}+\ldots+\dfrac{1}{30}\\~~~~~~~~\texttt{de~10~ori}\\\dfrac{10}{30}<\dfrac{1}{21}+\dfrac{1}{22}+\ldots+\dfrac{1}{30}\\\\\dfrac{1}{3}<\dfrac{1}{21}+\dfrac{1}{22}+\ldots+\dfrac{1}{30}[/tex]
[tex]\texttt{Pe de alta parte:}\\\dfrac{1}{21}<\dfrac{1}{20}\\\\\dfrac{1}{22}<\dfrac{1}{20}\\~~~~~~\vdots\\\dfrac{1}{30}<\dfrac{1}{20}\\\\\dfrac{1}{21}+\dfrac{1}{22}+\ldots+\dfrac{1}{30}<\underbrace{\dfrac{1}{30}+\dfrac{1}{30}+\dfrac{1}{30}+\ldots+\dfrac{1}{30}}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\texttt{de 10 ori}\\\dfrac{1}{21}+\dfrac{1}{22}+\ldots+\dfrac{1}{30}<\dfrac{10}{20}\\\\\dfrac{1}{21}+\dfrac{1}{22}+\ldots+\dfrac{1}{30}<\dfrac{1}{2}[/tex]
