Đáp án:

 $ \dfrac{1}{3}+\dfrac{1}{16}+\dfrac{1}{19}+\dfrac{1}{21}+\dfrac{1}{64}+\dfrac{1}{72}+\dfrac{1}{83}+\dfrac{1}{94}<\dfrac{3}{5}$

Giải thích các bước giải:

$64<72<83<94\\
\Rightarrow \dfrac{1}{64}>\dfrac{1}{72}>\dfrac{1}{83}>\dfrac{1}{94}\\
\dfrac{1}{72}<\dfrac{1}{64}\\
\dfrac{1}{83}<\dfrac{1}{64}\\
\dfrac{1}{94}<\dfrac{1}{64}\\
\Rightarrow \dfrac{1}{64}+\dfrac{1}{72}+\dfrac{1}{83}+\dfrac{1}{94}<4.\dfrac{1}{64}<\dfrac{4}{60}=\dfrac{1}{15}\\
\dfrac{1}{16}>\dfrac{1}{19}>\dfrac{1}{21}\\
\Rightarrow \dfrac{1}{16}+\dfrac{1}{19}+\dfrac{1}{21}<3.\dfrac{1}{16}<3.\dfrac{1}{15}=\dfrac{3}{15}\\
\Rightarrow \dfrac{1}{3}+\dfrac{1}{16}+\dfrac{1}{19}+\dfrac{1}{21}+\dfrac{1}{64}+\dfrac{1}{72}+\dfrac{1}{83}+\dfrac{1}{94}<\dfrac{1}{15}+\dfrac{3}{15}+\dfrac{1}{3}=\dfrac{3}{5}$

Đáp án:

 $\text{Chúc bạn học tốt}$

Giải thích các bước giải:

 $M=\dfrac{1}{3}+\dfrac{1}{16}+\dfrac{1}{19}+\dfrac{1}{21}+\dfrac{1}{64}+\dfrac{1}{72}+\dfrac{1}{83}+\dfrac{1}{94}$

$⇒M=\dfrac{1}{3}+(\dfrac{1}{16}+\dfrac{1}{19}+\dfrac{1}{21})+(\dfrac{1}{64}+\dfrac{1}{72}+\dfrac{1}{83}+\dfrac{1}{94})$

Xét $\dfrac{1}{16}+\dfrac{1}{19}+\dfrac{1}{21}$

$⇒\dfrac{1}{16}+\dfrac{1}{19}+\dfrac{1}{21}<\dfrac{1}{15}+\dfrac{1}{15}+\dfrac{1}{15}$

$⇒\dfrac{1}{16}+\dfrac{1}{19}+\dfrac{1}{21}<3×\dfrac{1}{15}$

$⇒\dfrac{1}{16}+\dfrac{1}{19}+\dfrac{1}{21}<\dfrac{1}{5}$

Xét $\dfrac{1}{64}+\dfrac{1}{72}+\dfrac{1}{83}+\dfrac{1}{94}$

$⇒\dfrac{1}{64}+\dfrac{1}{72}+\dfrac{1}{83}+\dfrac{1}{94}<\dfrac{1}{60}+\dfrac{1}{60}+\dfrac{1}{60}+\dfrac{1}{60}$

$⇒\dfrac{1}{64}+\dfrac{1}{72}+\dfrac{1}{83}+\dfrac{1}{94}<4×\dfrac{1}{60}$

$⇒\dfrac{1}{64}+\dfrac{1}{72}+\dfrac{1}{83}+\dfrac{1}{94}<\dfrac{1}{15}$

Do đó:$M<\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{15}$

$⇒M<\dfrac{3}{5}$

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