Tính nhanh: \(\Large A = \dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac

Tính  nhanh:

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

(Điền kết quả dưới dạng phân số tối giản a/b)

• A. 63/64

Ta có

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

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

\(\Large 2\times A =1+ \dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}\)

 Ta có: 

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

\(\Large A = 1-\dfrac{1}{64}\)

\(\Large A = \dfrac{63}{64}\)