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NT
0
NT
0
H9
HT.Phong (9A5)
CTVHS
22 tháng 6 2023
\(A=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{99}}\)
\(\Rightarrow\dfrac{A}{3}=\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{100}}\)
\(\Rightarrow A-\dfrac{A}{3}=\dfrac{2A}{3}=\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{99}}\right)-\left(\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{100}}\right)\)
\(\Rightarrow\dfrac{2A}{3}=\left(\dfrac{1}{3^2}-\dfrac{1}{3^2}\right)+\left(\dfrac{1}{3^3}-\dfrac{1}{3^3}\right)+...+\left(\dfrac{1}{3^{99}}-\dfrac{1}{3^{99}}\right)+\left(\dfrac{1}{3}-\dfrac{1}{3^{100}}\right)=\dfrac{1}{3}-\dfrac{1}{3^{100}}\)
\(\Rightarrow2A=3\cdot\left(\dfrac{1}{3}-\dfrac{1}{3^{100}}\right)\)
\(\Rightarrow\text{A}=\dfrac{1-\dfrac{1}{3^{99}}}{2}\)
\(\Rightarrow A=\dfrac{1}{2}-\dfrac{1}{2.3^{99}}< \dfrac{1}{2}\)
11 tháng 8 2019
a, \(\frac{22}{5}+\frac{1}{2}\cdot x^2=4\cdot\frac{8}{5}\)
=> \(\frac{22}{5}+\frac{1}{2}\cdot x^2=\frac{32}{5}\)
=> \(\frac{1}{2}\cdot x^2=\frac{32}{5}-\frac{22}{5}\)
=> \(\frac{1}{2}\cdot x^2=2\)
=> \(x^2=2:\frac{1}{2}=4\)
=> x = 2 hoặc x = -2
\(b,\frac{7}{2}-\left|x-\frac{1}{3}\right|=\frac{5}{2}\)
=> \(\left|x-\frac{1}{3}\right|=\frac{7}{2}-\frac{5}{2}\)
=> \(\left|x-\frac{1}{3}\right|=1\)
=> \(x-\frac{1}{3}=1\)hoặc \(x-\frac{1}{3}=-1\)
=> x = 1 + 1/3 hoặc x = -1 + 1/3
=> x = 4/3 hoặc x = -2/3
c, \(\left[x-\frac{1}{2}\right]\left[-3-\frac{x}{2}\right]=0\)
=> x - 1/2 = 0 hoặc -3 - x/2 = 0
=> x = 0 + 1/2 hoặc x/2 = -3
=> x = 1/2 hoặc x = -6
30 tháng 9 2021
A=\(2^2-9^3+4^{-2}.16-2.5^2\)
\(=4-729+1-50=-774\)
B=\(\left(2^3.2\right).\dfrac{1}{2}+3^{-2}.3^2-7.1+5\)
\(B=2^4.\dfrac{1}{2}+1-7+5=8+1-7+5=7\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
16 tháng 8
C = 2-3 + (52)3.5-3 + 4-3.16 - 2.32 - 105.(\(\dfrac{24}{51}\))0
C = \(\dfrac{1}{8}\) + 56.5-3 + 4-3.42 - 2.9 - 105.1
C = \(\dfrac{1}{8}\) + 53 + \(\dfrac{1}{4}\) - 18 - 105
C = (\(\dfrac{1}{8}\) + \(\dfrac{1}{4}\)) - (105 - 125 + 18)
C = \(\dfrac{3}{8}\) - (-20 + 18)
C = \(\dfrac{3}{8}\) + 2
C = \(\dfrac{19}{8}\)
16 tháng 6 2022
\(\Leftrightarrow\left(2x+3;-2y+5\right)\in\left\{\left(1;-7\right);\left(-7;1\right);\left(-1;7\right);\left(7;-1\right)\right\}\)
hay \(\left(x,y\right)\in\left\{\left(-1;6\right);\left(-5;2\right);\left(-2;-1\right);\left(2;2\right)\right\}\)
9 tháng 11 2021
\(1,\Leftrightarrow\left[{}\begin{matrix}2x-1=5\\1-2x=5\end{matrix}\right.\Leftrightarrow D\\ 2,\Leftrightarrow\left(-3\right)^x=-27\cdot81=-2187=\left(-3\right)^7\\ \Leftrightarrow x=7\left(A\right)\)
QT
1
2 tháng 7 2023
a: =>\(4\cdot3^x\cdot\dfrac{1}{3}+2\cdot3^x\cdot9=4\cdot3^6+2\cdot3^9\)
=>3^x(4*1/3+2*9)=3^6(4+2*3^3)
=>3^x*58/3=3^6*58
=>3^x/3^6=3
=>x-6=1
=>x=7
b: =>\(2^x\cdot\left(\dfrac{1}{5}+\dfrac{1}{3}\cdot2\right)=2^7\left(\dfrac{1}{5}+\dfrac{1}{3}\cdot2\right)\)
=>2^x=2^7
=>x=7
28 tháng 8 2016
a) \(\left(\frac{-2}{3}+\frac{3}{7}\right):\frac{4}{5}+\left(\frac{-1}{3}+\frac{4}{7}\right):\frac{4}{5}\)
\(=\left(\frac{-2}{3}+\frac{3}{7}+\frac{-1}{3}+\frac{4}{7}\right):\frac{4}{5}\)
\(=\left(-1+1\right):\frac{4}{5}\)
\(=0:\frac{4}{5}\)
\(=0\)
b) \(\frac{5}{9}:\left(\frac{1}{11}-\frac{5}{22}\right)+\frac{5}{9}:\left(\frac{1}{15}-\frac{2}{3}\right)\)
\(=\frac{5}{9}:\frac{-3}{22}+\frac{5}{9}:\frac{-3}{5}\)
\(=\frac{5}{9}.\frac{-22}{3}+\frac{5}{9}.\frac{-5}{3}\)
\(=\frac{5}{9}.\left(\frac{-22}{3}+\frac{-5}{3}\right)\)
\(=\frac{5}{9}.-9\)
\(=-5\)