\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)

\(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\)

\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\right)\)

\(2A=1-\frac{1}{3^8}\)

\(A=\frac{1}{2}-\frac{1}{2.3^8}\)

Ta có: \(\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\cdot\ldots\cdot\left(1-\frac{1}{200^2}\right)\)

\(=\left(1-\frac12\right)\left(1-\frac13\right)\cdot\ldots\cdot\left(1-\frac{1}{200}\right)\left(1+\frac12\right)\left(1+\frac13\right)\cdot\ldots\cdot\left(1+\frac{1}{200}\right)\)

\(=\frac12\cdot\frac23\cdot\ldots\cdot\frac{199}{200}\cdot\frac32\cdot\frac43\cdot\ldots\cdot\frac{201}{200}=\frac{1}{200}\cdot\frac{201}{2}=\frac{201}{400}>\frac{200}{400}=\frac12\)

3 . ( 2x - 1 ) - 2 = 13 

3 . ( 2x - 1 ) = 12 + 3 

3 . ( 2x - 1 ) = 15 

      2x - 1 = 15 : 3 

      2x - 1 = 5 

     2x = 5 + 1 = 6 

x = 6 : 2 = 3 

Vậy x = 3

\(3\left(2x-1\right)-2=13\)

\(3\left(2x-1\right)=15\)

\(2x-1=5\)

\(2x=6\)

\(x=3\)

mk ko bt

2^2.3^1-(1^2021+2021^2) : (-2)

= 4.3-(1+4084441 ) : (-2)

= 12-4084442:(-2)

= 12-(-2042221)

= 20421133

\(\dfrac{1}{2}\left(x-2\right)+\dfrac{1}{3}\left(2-x\right)=x\\ \Leftrightarrow\dfrac{1}{2}\left(x-2\right)-\dfrac{1}{3}\left(x-2\right)=x\\ \Leftrightarrow\left(x-2\right).\left(\dfrac{1}{2}-\dfrac{1}{3}\right)=x\\ \Leftrightarrow\left(x-2\right).\left(\dfrac{3-2}{6}\right)=x\\ \Leftrightarrow\left(x-2\right).\dfrac{1}{6}=x\\ \Leftrightarrow\dfrac{1}{6}x-\dfrac{1}{3}-x=0\\ \Leftrightarrow\left(\dfrac{1}{6}-1\right)x=\dfrac{1}{3}\\ \Leftrightarrow\left(\dfrac{1-6}{6}\right)x=\dfrac{1}{3}\\ \Leftrightarrow\dfrac{-5}{6}x=\dfrac{1}{3}\\ \Leftrightarrow x=\dfrac{1}{3}:\left(-\dfrac{5}{6}\right)\\ \Leftrightarrow x=-\dfrac{2}{5}\)

Vậy \(x=-\dfrac{2}{5}\)

x= \(\dfrac{7\pm\sqrt{37}}{3}\) nha

khó quá nhiw

\(A=\frac{2^{19}\cdot27^3+15\cdot4^9\cdot9}{6^9\cdot2^{10}}+1^{210}\)

\(=\frac{2^{19}\cdot3^9+2^{18}\cdot3^3\cdot5}{2^9\cdot3^9\cdot2^{10}}+1\)

\(=\frac{2^{18}\cdot3^3\left(3^6+5\right)}{2^{19}\cdot3^9}+1=\frac{3^6+5}{3^6}+1=\frac{2\cdot3^6+5}{3^6}=\frac{1463}{729}\)

\(\text{[}2^2+2^1+2^2+2^3\text{]}.2^0.2^1.2^2.2^3\)

\(=\left(4+2+4+8\right).1.2.4.8\)

\(=\left(8+10\right).2.32\)

\(=18.64=1152\)

Chúc bạn học tốt  (Cách này k đc nhanh lắm)