Giup mk câu này nha, tuy nhìn hơi rối Cho M= 1/3 + 1/16 + 1/19 + 1/21+ 1/64 + 1/72 + 1/83 + 1/94 14/08/2021 Bởi Claire Giup mk câu này nha, tuy nhìn hơi rối Cho M= 1/3 + 1/16 + 1/19 + 1/21+ 1/64 + 1/72 + 1/83 + 1/94
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: $64<72<83<94\\\Rightarrow \dfrac{1}{64}>\dfrac{1}{72}>\dfrac{1}{83}>\dfrac{1}{94}\\\dfrac{1}{72}<\dfrac{1}{64}\\\dfrac{1}{83}<\dfrac{1}{64}\\\dfrac{1}{94}<\dfrac{1}{64}\\\Rightarrow \dfrac{1}{64}+\dfrac{1}{72}+\dfrac{1}{83}+\dfrac{1}{94}<4.\dfrac{1}{64}<\dfrac{4}{60}=\dfrac{1}{15}\\\dfrac{1}{16}>\dfrac{1}{19}>\dfrac{1}{21}\\\Rightarrow \dfrac{1}{16}+\dfrac{1}{19}+\dfrac{1}{21}<3.\dfrac{1}{16}<3.\dfrac{1}{15}=\dfrac{3}{15}\\\Rightarrow \dfrac{1}{3}+\dfrac{1}{16}+\dfrac{1}{19}+\dfrac{1}{21}+\dfrac{1}{64}+\dfrac{1}{72}+\dfrac{1}{83}+\dfrac{1}{94}<\dfrac{1}{15}+\dfrac{3}{15}+\dfrac{1}{3}=\dfrac{3}{5}$ Bình luận
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:$M<\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{15}$ $⇒M<\dfrac{3}{5}$ Vậy đpcm Bình luận
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:$M<\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{15}$
$⇒M<\dfrac{3}{5}$
Vậy đpcm