nhân A lên 2A sau đó lấy 2A-A là đc :

2A =1+1/2+.....+1/32

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

A=1-1/64

A=63/64

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

\(2A=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)\times2\)

\(2A=\frac{1}{2}\times2+\frac{1}{4}\times2+\frac{1}{8}\times2+\frac{1}{16}\times2+\frac{1}{32}\times2+\frac{1}{64}\times2\)

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

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

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

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

Lời giải:

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

$2\times A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}$

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

$A=1-\frac{1}{64}=\frac{63}{64}$

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)
            = 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
         = 63/64

Cộng thêm 1/2 vào biểu thức đã cho, có:

S + 1/2= 1/2+1/4+ 1/8+ 1/16+1/32+1/64+1/128

Nhận xét:

Ta có : A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64

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

=> 2A - A = 1 - 1/64

=> A = 1 - 1/64

=> A = 63/64

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

\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)

\(\Rightarrow2A-A=1-\frac{1}{128}=\frac{127}{128}\)

=127/128 nhe 

dề có sai ko

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

B=1/2+1/2^2+1/2^3+1/2^4+1/2^5+1/2^6

=>2B=1+1/2+1/2^2+...1/3^5

=>2B-B=1-1/2^6

=>B=1-1/64

=>B=63/64

- Tính A x 2

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

- Tính A bằng cách A = A x 2 – A

Vậy  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+1/8+1/16+1/32+1/64.Ta có:

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

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

A x 2-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=63/64

Ai đi qua cho mình xin cái k mình k lại cho
 

- Tính A x 2

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

- Tính A bằng cách A = A x 2 – A

Vậy  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

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

S=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32+1/32-1/64

S=1-1/64

S=63/64

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

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

2S =1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32

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

S = 1 - 1/64

S = 63/64

Tính không quy đồng mẫu:

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

\(A=1-\frac{1}{64}=\frac{63}{64}\)

A = 32 + 16 + 8 + 4 + 2 + 1/64 = 63/64

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