Tính biểu thức sau: 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256
Tính biểu thức sau: \(\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + \frac{1}{{64}} + \frac{1}{{128}} + \frac{1}{{256}}\).
Lời giải:
Đặt A = \(\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + \frac{1}{{64}} + \frac{1}{{128}} + \frac{1}{{256}}\)
\( \Rightarrow \) 2A = \(1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + \frac{1}{{64}} + \frac{1}{{128}}\)
\( \Rightarrow \) 2A − A = 1 − \(\frac{1}{{256}}\)
\( \Rightarrow \) A = \(\frac{{255}}{{256}}\)