2

4

8

16

32

64

128

256

512

1024

2048

4096

8192

1+1=2

2+2=4

4+4=8

8+8=16

16+16=32

64+64=128

128+128=256

512+512=1024

2048+2048=4096

xong

1+1=2

2+2=4

4+4=8

8+8=16

16+16=32

32+32=64

64+64=128

128+128=256

256+256=512

512+512=1024

1024+1024=2048

2048+2048=4096

4096+4096=8192

M = 1/4 + 1/16 + 1/64 + 1/256 + 1/1024 
4.M = 1 + 1/4 + 1/16 + 1/64 + 1/256 
4M - M = (1 + 1/4 + 1/16 + 1/64 + 1/256 ) - ( 1/4 + 1/16 + 1/64 + 1/256 + 1/1024 ) 
3M       = 1 - 1/1024 
 3M       = 1023/1024 
  M        = 341/1024

M=\(\dfrac{1}{4}\)+\(\dfrac{1}{16}\)+\(\dfrac{1}{64}\)+\(\dfrac{1}{256}\)+\(\dfrac{1}{1024}\)

  =\(\dfrac{1}{4}\)+\(\dfrac{1}{4^2}\)+\(\dfrac{1}{4^3}\)+\(\dfrac{1}{4^4}\)+\(\dfrac{1}{4^5}\)

=>4M=1+\(\dfrac{1}{4}\)+\(\dfrac{1}{4^2}\)+\(\dfrac{1}{4^3}\)+\(\dfrac{1}{4^4}\)

=>4M-M=3M=(1+\(\dfrac{1}{4}\)+\(\dfrac{1}{4^2}\)+\(\dfrac{1}{4^3}\)+\(\dfrac{1}{4^4}\))-(\(\dfrac{1}{4}\)+\(\dfrac{1}{4^2}\)+\(\dfrac{1}{4^3}\)+\(\dfrac{1}{4^4}\)+\(\dfrac{1}{4^5}\))=1-\(\dfrac{1}{4^5}\)=\(\dfrac{1023}{1024}\)

=>M=\(\dfrac{1023}{1024}\):3=\(\dfrac{341}{1024}\)

`@` `\text {Ans}`

`\downarrow`

\(M=\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{64}+\dfrac{1}{256}+\dfrac{1}{1024}\)

\(\Rightarrow4M=1+\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{64}+\dfrac{1}{256}\)

\(\Rightarrow4M-M=\) \(\left(1+\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{64}+\dfrac{1}{256}\right)-\left(\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{64}+\dfrac{1}{256}+\dfrac{1}{1024}\right)\)

\(=\) \(1+\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{64}+\dfrac{1}{256}-\dfrac{1}{4}-\dfrac{1}{16}-\dfrac{1}{64}-\dfrac{1}{256}-\dfrac{1}{1024}\)

\(=1-\dfrac{1}{1024}\)

\(=\dfrac{1024}{1024}-\dfrac{1}{1024}=\dfrac{1023}{1024}\)

`4M - M = 3M`

 \(\Rightarrow3M=\dfrac{1023}{1024}\) 

\(\Rightarrow M=\dfrac{1023}{1024}\div3\)

\(\Rightarrow M=\dfrac{341}{1024}\)

Vậy, `M = `\(\dfrac{341}{1024}\)

Đặt 

\(S=1+2+4+...+2048+4096\)

\(S=1+2^1+2^2+...+2^{11}+2^{12}\)

\(2S=2+2^2+2^3+...+2^{12}+2^{13}\)

\(2S-S=\left(2+2^2+2^3+...+2^{13}\right)-\left(1+2+2^2+..+2^{12}\right)\)

\(S=2^{13}-1=8192-1=8191\)

Gọi A=1+2+4+8+16+...+1024+2048+4096

2A=2+4+8+16+32+...+2048+4096+8192

2A-A=(2+4+8+16+32+...+2048+4096+8192)-(1+2+4+8+16+...+1024+2048+4096)

A=8192-1

A=8191

                Đặt A = 1 + 2 + 4 + 8 + 16 +...+ 1024 + 2048 + 4096

                A = 1 + 2 + 2² + 2³ + 2⁴ +.... + 2¹⁰ + 2¹¹ + 2¹²

                     2A = 2 + 2² + 2³ + 2⁴ + 2⁵ + ..... + 2¹¹ + 2¹² + 2¹³

               2A - A = (2 + 2² + 2³ + 2⁴ + .... + 2¹¹ + 2¹² + 2¹³) - (1 + 2 + 2² + 2³ + 2⁴ +.....+ 2¹⁰ + 2¹¹ + 2¹²)

              => A = 2¹³ - 1

              => A = 8192 - 1 = 8191

           Ủng hộ mk nha !!! ^_^

Mình nghĩ đây là nâng cao tiểu học 
Đặt S = 1/2 + 1/4 + 1/8 + 1/16 + ... 
==> 2S = 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... 
2S = 1 + S 
==> S = 1 
Đây cũng là kết quả khi tính theo cấp số nhân khi n --> vô cùng

2A=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512

2A-A=1-1/1024

A=1-1/1024

A=1023/1024

\(=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\)

\(2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)

\(2A-A=1-\frac{1}{2^{10}}\)

\(\Rightarrow A=\frac{1}{2^{10}-1}\)\(=\frac{1}{1023}\)

nha

=1365/4096 nha bn

Bạn đặt biểu thức trên là A

Nhân tất cả với 4 thì là 4A

Lấy 4A-A thì là 3A=1-1/4096

Từ đó tính A bạn nhé

tính nhanh 1/4+1/16+1/64+...+1/4096+1/76394 cứu mình với

2047/4096

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