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: 

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

$\Large A = 1-\dfrac{1}{64}$

$\Large A = \dfrac{63}{64}$