Tính gái trị biểu thức: $\dfrac{2}{3}$ + $\dfrac{2}{6}$ + $\dfrac{2}{12}$ + $\dfrac{2}{24}$ + $\dfrac{2}{48}$ + $\dfrac{2}{96}$ + $\dfrac{2}{192}$ ~ HELP ~

Đáp án: $\dfrac{254}{192}$

Giải thích các bước giải:

$\dfrac{2}{3}$ + $\dfrac{2}{6}$ + $\dfrac{2}{12}$ + $\dfrac{2}{24}$ + $\dfrac{2}{48}$ + $\dfrac{2}{96}$ + $\dfrac{2}{192}$

Đặt A $\times$ 2 = $\dfrac{4}{3}$ + $\dfrac{4}{6}$ + $\dfrac{4}{12}$ + $\dfrac{4}{24}$ + $\dfrac{4}{24}$ + $\dfrac{4}{48}$ + $\dfrac{4}{96}$ + $\dfrac{4}{192}$

A $\times$ 2 = $\dfrac{4}{3}$ + $\dfrac{1}{3}$ + $\dfrac{2}{3}$ + $\dfrac{2}{6}$ + $\dfrac{2}{12}$ + $\dfrac{2}{24}$ + $\dfrac{2}{48}$ + $\dfrac{2}{96}$

A $\times$ 2 = $\dfrac{4}{3}$ + A - $\dfrac{2}{192}$ 

A = $\dfrac{4}{3}$ - $\dfrac{2}{192}$ (Cùng bớt 2 vế đi A)

A = $\dfrac{127}{96}$