Đặt tổng trên = A

\(A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{4096}+\frac{1}{8192}\)

\(A.2=2+1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2048}+\frac{1}{4096}\)

\(A.2-A=\left(2+1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2048}+\frac{1}{4096}\right)-\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{4096}+\frac{1}{8192}\right)\)

\(A=2-\frac{1}{8192}=\frac{16383}{8192}\)
 

Đặt A = 1 + 1/2 + 1/4 + 1/8 + ... + 1/4096 + 1/8192

2A = 2 + 1 + 1/2 + 1/4 + ... + 1/2048 + 1/4096

2A - A = (2 + 1 + 1/2 + 1/4 + ... + 1/2048 + 1/4096) - (1 + 1/2 + 1/4 + 1/8 +... + 1/4096 + 1/8192)

A = 2 - 1/8192

A = 16383/8192

\(\text{Đ}\text{ặt}:A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{4096}+\frac{1}{8192}\)

\(2A=2+1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2048}+\frac{1}{4096}\)

\(2A-A=\left(2+1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2048}+\frac{1}{4096}\right)-\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{4096}+\frac{1}{8192}\right)\)

\(A=2-\frac{1}{8192}=\frac{16383}{8192}\)

A=1+2+2^2+...+2^13

=>2A=2+2^2+...+2^14

=>2A-A=2^14-1

=>A=2^14-1

Đặt A=\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+................+\frac{1}{2048}+\frac{1}{4096}\)

2A=\(1+\frac{1}{2}+\frac{1}{4}+....................+\frac{1}{1024}+\frac{1}{2048}\)

2A-A=\(\left(1+\frac{1}{2}+\frac{1}{4}+................+\frac{1}{1024}+\frac{1}{2048}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...............+\frac{1}{2048}+\frac{1}{4096}\right)\)

A=\(1-\frac{1}{4096}\)

A=\(\frac{4095}{4096}\)

4095/4096 đó lam lợn hả

các bạn sai rồi bằng 2047/2048 đó chắc chắn 100% luôn mk thi rồi.

Đúng thì nhớ k nha các bạn hihi ^-^

bn tham khảo tại link này nhé :

https://olm.vn/hoi-dap/question/656309.html

https://olm.vn/hoi-dap/question/656309.html

Từ biểu thức trên ta được

A=1/2+1/2^2+1/2^3+....+1/2^11+1/2^12

2A-A=2(1/2+1/2^2+1/2^3+....+1/2^11+1/2^12)-(1/2+1/2^2+1/2^3+....+1/2^11+1/2^12)

A=1+1/2^2+1/2^3+....+1/2^11-1/2-1/2^2-...-1/2^12

A=1/2-1/2^12

Ủng hộ cho mình nha bạn

\(A=\)\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}+\frac{1}{2048}+\frac{1}{4096}\)

\(A=\)\(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{12}}\)

\(2A=\)\(2\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{12}}\right)\)

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

\(2A-A=\)\(\left(1+\frac{1}{2}+...+\frac{1}{2^{11}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{12}}\right)\)

\(A=1-\frac{1}{2^{12}}\)

Ta thấy:

1 + 2 = 3 ( Số liền trước 4)

1 + 2 + 4 = 7 ( Số liền trước 8)

1 + 2 + 4 + 8 = 15 ( Số liền trước 16)

⇒ 1 + 2 + 4 + 8 + 16 +……. + 4096 sẽ bằng số liền trước 8192

Mà số liền trước 8192 là 8191

⇒ A = 8191 + 8192 = 16383

Vậy A = 16383.

Đặt A=1/2+1/4+1/8+1/16+1/32+...+1/2048+1/4096

\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{12}}\)

\(2A=2\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{12}}\right)\)

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

\(2A-A=\left(1+\frac{1}{2}+...+\frac{1}{2^{11}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{12}}\right)\)

\(A=1-\frac{1}{2^{12}}\)

\(A=1+2+4+8+...+8192\)

\(2A=2+4+8+...+16384\)

\(2A-A=\left(2+4+...+16384\right)-\left(1+2+...+8192\right)\)

\(A=16384-1\)

\(A=16383\)

Thank you