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A = 2⁰ + 2¹ + 2² + 2³ + ... + 2²⁰¹⁰
⇒ 2A = 2 + 2² + 2³ + 2⁴ + ... + 2²⁰¹¹
⇒ A = 2A - A = (2 + 2² + 2³ + 2⁴ + ... + 2²⁰¹¹) - (2⁰ + 2¹ + 2² + 2³ + ... + 2²⁰¹⁰)
= 2²⁰¹¹ - 2⁰
= 2²⁰¹¹ - 1
= B
Vậy A = B
\(a,\Rightarrow2A=2+2^2+...+2^{2011}\)
\(\Rightarrow2A-A=2+2^2+...+2^{2011}-2^0-2-..-2^{2010}\)
\(\Rightarrow A=2^{2011}-1=B\)
\(b,A=2019.2011=\left(2010-1\right)\left(2010+1\right)=\left(2010-1\right).2010+\left(2010-1\right)=2010^2-2010+2010-1=2010^2-1< 2010^2=B\)
\(a,\Rightarrow2A=2^1+2^2+...+2^{2011}\\ \Rightarrow2A-A=A=2^{2011}-2^0=2^{2011}-1=B\)
\(b,A=\left(2010-1\right)\left(2010+1\right)=2010^2+2010-2010-1=2010^2-1< 2010^2=B\)
Bài 2 :
a, \(x=\dfrac{3}{5}-\dfrac{7}{8}=\dfrac{24-30}{40}=-\dfrac{6}{40}=-\dfrac{3}{20}\)
b, \(2x-1=-2\Leftrightarrow x=-\dfrac{1}{2}\)
a) \(-2011-\left(200-2011\right)\)
\(=-2011-200+2011\)
\(=\left(-2011+2011\right)-200\)
\(=0-200\)
\(=-200\)
b) \(\left(-2\right)^2-\left(-2000\right)^0+\left(-1\right)^{2018}-\left|-20\right|\)
\(=4-1+1-20\)
\(=4-20\)
\(=-16\)
Bài 1 :
\(a)-2011-(200-2011)\)
\(=-2011-(200+2011)\)
\(=(-2011+2011)-200\)
\(=0-200=-200\)
\(b)(-2)^2-(-2000)^0+(-1)^{2018}-\left|-20\right|\)
\(=4-1+1-20\)
\(=4-20=-16\)
\(c)23\cdot18-23\cdot26+(-23)\cdot2\)
\(=23\cdot(18-26)+-(23\cdot2)\)
\(=23\cdot(-8)+(-46)\)
\(=-230\)
Bài 2 : Tìm số nguyên x biết :
\(a)3x-(-5)=20\)
\(\Rightarrow3x+5=20\)
\(\Rightarrow3x=20-5\)
\(\Rightarrow3x=15\Rightarrow x=5\)
\(b)3(x+2)=-4+(-2)^3\)
\(\Rightarrow3(x+2)=-4+(-8)\)
\(\Rightarrow3(x+2)=-12\)
\(\Rightarrow x+2=-12\div3\)
\(\Rightarrow x+2=-4\)
Tự tìm x câu b, và câu c,
Bài 3 tự làm
Bài 1
a) S = 1 + 2 + 2² + 2³ + ... + 2²⁰²³
2S = 2 + 2² + 2³ + 2⁴ + ... + 2²⁰²⁴
S = 2S - S = (2 + 2² + 2³ + ... + 2²⁰²⁴) - (1 + 2 + 2² + 2³)
= 2²⁰²⁴ - 1
b) B = 2²⁰²⁴
B - 1 = 2²⁰²⁴ - 1 = S
B = S + 1
Vậy B > S
a,
\(S=1+2+2^2+...+2^{2023}\)
\(2S=2+2^2+2^3+...+2^{2024}\)
\(\Rightarrow S=2^{2024}-1\)
b.
Do \(2^{2024}-1< 2^{2024}\)
\(\Rightarrow S< B\)
2.
\(H=3+3^2+...+3^{2022}\)
\(\Rightarrow3H=3^2+3^3+...+3^{2023}\)
\(\Rightarrow3H-H=3^{2023}-3\)
\(\Rightarrow2H=3^{2023}-3\)
\(\Rightarrow H=\dfrac{3^{2023}-3}{2}\)
Bài 1:
a) Ta có: \(\left|x-4\right|=\left|-81\right|\)
\(\Leftrightarrow\left|x-4\right|=81\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=81\\x-4=-81\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=85\\x=-77\end{matrix}\right.\)
Vậy: \(x\in\left\{-77;85\right\}\)
b) Ta có: \(\left(x-2\right)\left(y+1\right)=23\)
\(\Leftrightarrow x-2;y+1\inƯ\left(23\right)\)
\(\Leftrightarrow x-2;y+1\in\left\{1;23;-1;-23\right\}\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left\{{}\begin{matrix}x-2=1\\y+1=23\end{matrix}\right.\\\left\{{}\begin{matrix}x-2=23\\y+1=1\end{matrix}\right.\\\left\{{}\begin{matrix}x-2=-1\\y+1=-23\end{matrix}\right.\\\left\{{}\begin{matrix}x-2=-23\\y+1=-1\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left\{{}\begin{matrix}x=3\\y=22\end{matrix}\right.\\\left\{{}\begin{matrix}x=25\\y=0\end{matrix}\right.\\\left\{{}\begin{matrix}x=1\\y=-24\end{matrix}\right.\\\left\{{}\begin{matrix}x=-21\\y=-2\end{matrix}\right.\end{matrix}\right.\)
Vậy: (x,y)\(\in\){(3;22);(25;0);(1;-24);(-21;-2)}