\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{2048}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-...-\frac{1}{2048}+\frac{1}{2048}\)

\(=1-\frac{1}{2048}\)

\(=\frac{2047}{2048}\)

k mk nha

Đặt A = 1/2¹ + 1/2² + 1/2³ + 1/2⁴ +... +1/2¹¹

 2A = (1/2¹ + 1/2² + 1/2³ + 1/2⁴ +... +1/2¹¹⁾.2

2A =  1 + 1/2 +1/2² + ...+ 1/2¹⁰

2A - A = ( 1 + 1/2 +1/2² + ...+ 1/2¹⁰ ) -  (1/2¹ + 1/2² + 1/2³ + 1/2⁴ +... +1/2¹¹)

A = 1 - 1/2¹¹

A = 1 - 1/2048

A = 2047/2048

NHA CÁC BẠN ^_^

= 2047/2048 nha bạn k mình nha 

1024 phan 2048

Đặt: \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2048}\)

\(\Rightarrow A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{11}}\)

\(\Rightarrow2A=2\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{11}}\right)\)

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

\(\Rightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{10}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{11}}\right)\)

\(\Rightarrow A=1-\frac{1}{2^{11}}=\frac{2^{11}-1}{2^{11}}=\frac{2047}{2048}\)
 

\(2A=1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1024}\)

\(2A-A=\left(1+...+\frac{1}{1024}\right)-\left(\frac{1}{2}+...+\frac{1}{2048}\right)\)

\(A=1-\frac{1}{2048}=\frac{2047}{2048}\)

gọi biểu thức là A

A=1/2+1/4+1/8+...+1/2048=1/2+1/2^2+1/2^3+...+1/2^10

=>2A=1+1/2+1/2^2+...+1/2^9

=>A=2A-A(bạn đặt cột dọc ra rồi sẽ thấy:1/2-1/2=0;1/2^2-1/2^2=0;...)Ta được kết quả bằng 1+1/2^10

Đặt A =1/2 + 1/4 + 1/8 + ...+ 1/1024 + 1/2048

A= 1/2 + 1/2^2 + 1/2^3+...+ 1/2^10 + 1/2^11

2A= 1 +1/2 + 1/2^2 +...+ 1/2^9 + 1/2^10

2A-A= (1 +1/2 + 1/2^2 +...+ 1/2^9 + 1/2^10) - (1/2 + 1/2^2 + 1/2^3+...+ 1/2^10 + 1/2^11)

A= 1+1/2 + 1/2^2 +...+ 1/2^9 + 1/2^10 - 1/2 - 1/2^2 - 1/2^3 - ...- 1/2^10 - 1/2^11

A= 1- 1/2^11

A= 2047/ 2048

\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{2048}\)

\(=1-\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2048}\)

\(=1-\frac{1}{2048}\)

\(=\frac{2047}{2048}\)

 NHận xét :

1/2 = 1 - 1/2

1/4 = 1/2 - 1/4

1/8 = 1/4 - 1/8

...................

1/2048 = 1/1024 - 1/2048

Vậy 1/2 + 1/4 + 1/8 + ... + 1/2048

= 1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 + ... - ... + 1/1024 - 1/2048

= 1 - 1/2048 = 2047/2048

\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+..+\frac{1}{2048}\)

\(=1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+..+\frac{1}{2048}\)

\(=1-\frac{1}{2048}\)

\(=\frac{2047}{2048}\)

2047/2048 nha bạn

31/11 nhen bạn bấm may tính ra liền

Ta có: 

1/2=1—1/2

1/4=1/2—1/4

…………

1/1024—1/2048=1/2048

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