Tính: `B = - 1/3 + 1/(3^2) - 1/(3^3) + ... + 1/(3^50) - 1/(3^51)`

Đáp án:

Giải thích các bước giải:

Ta có:

$B=-\dfrac13+\dfrac1{3^2}-\dfrac1{3^3}+...+\dfrac1{3^{50}}-\dfrac1{3^{51}}$

$=> 3B=-1+\dfrac13-\dfrac1{3^2}+...+\dfrac1{3^{49}}-\dfrac1{3^{50}}$

$=> B+3B=-1-\dfrac{1}{3^{51}}$

$=> 4B=-1-\dfrac{1}{3^{51}}$

$=> B=\dfrac14(-1-\dfrac{1}{3^{51}})$