1/2nhân 2/3 cộng 1/3 nhân 1/2
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\(2^3+3\cdot\left(\dfrac{1}{9}\right)^0-2^{-2}\cdot4+\left[\left(-2\right)^2:\dfrac{1}{2}\right]\cdot8\)
\(=8+3\cdot1-\dfrac{1}{4}\cdot4+\left(4:\dfrac{1}{2}\right)\cdot8\)
\(=8+3-\dfrac{4}{4}+4\cdot2\cdot8\)
\(=11-1+8\cdot8\)
\(=10+64\)
\(=74\)
\(=8+3-2^{-2}\cdot2^2+\left[4\cdot2\right]\cdot8\)
=11-1+8*8
=64+10=74
Lời giải:
$A=9+2.3^2+2.3^3+2.3^4+...+2.3^{2023}$
$A-9=2(3^2+3^3+3^4+...+3^{2023})$
$3(A-9)=2(3^3+3^4+3^5+...+3^{2024})$
$\Rightarrow 3(A-9)-(A-9)=2(3^{2024}-3^2)$
$2(A-9)=2.3^{2024}-18$
$\Rightarrow 2A-18=2.3^{2024}-18$
$\Rightarrow A=3^{2024}\vdots 3^{2023}$ (đpcm)
\(A=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+...+\dfrac{1}{18.19.20}\)
\(2A=\dfrac{3-1}{1.2.3}+\dfrac{4-2}{2.3.4}+\dfrac{5-3}{3.4.5}+...+\dfrac{20-18}{18.19.20}=\)
\(=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+...+\dfrac{1}{18.19}-\dfrac{1}{19.20}=\dfrac{1}{2}-\dfrac{1}{19.20}\)
\(\Rightarrow A=\left(\dfrac{1}{2}-\dfrac{1}{19.20}\right):2\)
1/2x2/3+1/3x1/2
=1/2x(2/3+1/3)
=1/2x1
=1/2