Question

arată că 1/3<1/21+1/22+...+1/30<1/2
DAU COROANA


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Answer 1

Răspuns:

Explicație pas cu pas:

$\dfrac{1}{30}<\dfrac{1}{21}\\\\\dfrac{1}{30}<\dfrac{1}{22}\\\\~~~~~~\vdots\\\dfrac{1}{30}\leq\dfrac{1}{30}\\\\\underbrace{\dfrac{1}{30}+\dfrac{1}{30}+\ldots+\dfrac{1}{30}}<\dfrac{1}{21}+\dfrac{1}{22}+\ldots+\dfrac{1}{30}\\~~~~~~~~\texttt{de~10~ori}\\\dfrac{10}{30}<\dfrac{1}{21}+\dfrac{1}{22}+\ldots+\dfrac{1}{30}\\\\\dfrac{1}{3}<\dfrac{1}{21}+\dfrac{1}{22}+\ldots+\dfrac{1}{30}$

$\texttt{Pe de alta parte:}\\\dfrac{1}{21}<\dfrac{1}{20}\\\\\dfrac{1}{22}<\dfrac{1}{20}\\~~~~~~\vdots\\\dfrac{1}{30}<\dfrac{1}{20}\\\\\dfrac{1}{21}+\dfrac{1}{22}+\ldots+\dfrac{1}{30}<\underbrace{\dfrac{1}{30}+\dfrac{1}{30}+\dfrac{1}{30}+\ldots+\dfrac{1}{30}}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\texttt{de 10 ori}\\\dfrac{1}{21}+\dfrac{1}{22}+\ldots+\dfrac{1}{30}<\dfrac{10}{20}\\\\\dfrac{1}{21}+\dfrac{1}{22}+\ldots+\dfrac{1}{30}<\dfrac{1}{2}$