Tính nhanh giá trị biểu thức sau đây: \(A = \dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{8} + \dfrac{1}{{16}} + \dfrac{1}{{32}} + \dfrac{1}{{64}} \)\(+ \dfrac{1}{{128}}\)

Ta nhận thấy:

\(\dfrac{1}{2} = 1 - \dfrac{1}{2};\dfrac{1}{4} = \dfrac{1}{2} - \dfrac{1}{4};\dfrac{1}{8} = \dfrac{1}{4} - \dfrac{1}{8};\)

\(\dfrac{1}{{16}} = \dfrac{1}{8} - \dfrac{1}{{16}};\,\,\dfrac{1}{{32}} = \dfrac{1}{{16}} - \dfrac{1}{{32}};\)

\(\dfrac{1}{{64}} = \dfrac{1}{{32}} - \dfrac{1}{{64}};\,\,\dfrac{1}{{128}} = \dfrac{1}{{64}} - \dfrac{1}{{128}}.\) 

\(A = 1 - \dfrac{1}{2} + \dfrac{1}{2} - \dfrac{1}{4} + \dfrac{1}{4} - \dfrac{1}{8} \) \(+ \dfrac{1}{8} - \dfrac{1}{{16}} + \dfrac{1}{{16}} - \dfrac{1}{{32}} + \dfrac{1}{{32}} - \dfrac{1}{{64}}\) \(  + \dfrac{1}{{64}} - \dfrac{1}{{128}}\)

\( A = 1 - \dfrac{1}{{128}}= \dfrac{{127}}{{128}}\)

127/128 nha

127/128 nha