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

\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)

\(\Rightarrow2A-A=1-\frac{1}{64}\)

\(\Rightarrow A=\frac{63}{64}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+..+\frac{1}{32}-\frac{1}{64}\)

\(A=1-\frac{1}{64}\)

\(A=\frac{63}{64}\)Đây là cách 1

\(Ax2=1+\left(\frac{1}{2}+...+\frac{1}{64}\right)-\frac{1}{64}\)

\(Ax2=1+A-\frac{1}{64}\)

\(Ax2-A=1-\frac{1}{64}\)

\(A=\frac{63}{64}\)Đây là cách 2

P/s: Làm 1 cách đc kh???

A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64

2A = 1/2 x 2 + 1/4 x 2 + 1/8 x 2 + 1/16 x 2 + 1/32 x 2 + 1/64 x 2

2A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32

2A - A = ( 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 ) - ( 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 )

A = 1 -  1/64

A = 63/64

đặt `A= 1/2 + 1/4 + 1/8 + 1/16+ 1/32 + 1/64`

`=> 2A = 2(1/2 + 1/4 + 1/8 + 1/16+ 1/32 + 1/64)`

`2A = 1+1/2 +1/4 +1/8+1/16 +1/32`

`=>A =2A -A =1+1/2 +1/4 +1/8+1/16 +1/32-1/2-1/4-1/8-1/16-1/32 -1/64`

`A = 1-1/64 = 64/64 -1/64 =63/64`

bằng 511/512

1/2+1/4+1/8+1/16+1/32+1/64

=(1/2+1/4+1/8)+(1/16+1/32+1/64)

=(4/8+2/8+1/8)+(4/64+2/64+1/64)

=7/8+7/64

=56/64+7/64

=63/64

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

    2 x B   = 1 + \(\dfrac{1}{2}\)+ \(\dfrac{1}{4}\)  +  \(\dfrac{1}{8}\) +  \(\dfrac{1}{16}\)+ \(\dfrac{1}{32}\)

2 x B - B = 1 - \(\dfrac{1}{64}\)

           B = \(\dfrac{63}{64}\)

Đặt A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256

=> 2A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128

=> 2A - A = (1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128) -                                     (1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256)

=> A = 1 - 1/256

=> A = 255/256

Vậy: ...