Đáp án + Giải thích các bước giải:

 `Ta` `có:`

$A = \frac{1}{3} + \frac{1}{3^2} + \frac{1}{3^3} + \dots + \frac{1}{3^8}$

$3 \cdot A = 3 \cdot \left( \frac{1}{3} + \frac{1}{3^2} + \frac{1}{3^3} + \dots + \frac{1}{3^8} \right)$

$3A = 1 + \frac{1}{3} + \frac{1}{3^2} + \dots + \frac{1}{3^7}$

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

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

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

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

`A=(6561-1)/(2.6561)`

`A=6560/13122=3280/6561`

`Vậy` `A=3280/6561`