A = 8 + 16 + 31 + 64 + ..... + 2048 + 4096

A = 2³ + 2⁴ + 2⁵ + 2⁶ + ..... + 2¹¹ + 2¹²

2A =  2⁴ + 2⁵ + 2⁶ + ..... + 2¹¹ + 2¹² + 2¹³

2A - A = (2⁴ + 2⁵ + 2⁶ + ..... + 2¹¹ + 2¹² + 2¹³) - (2³ + 2⁴ + 2⁵ + 2⁶ + ..... + 2¹¹ + 2¹²)

A = 2¹³ - 2³ = 4096.2 - 8 = 8192 - 8 = 8184

A= (4096+8)x[ ( 4096-8  ) : 8+1 ) :2

  = 4104  x [ 4088:8+1 ] : 2

  = 4104 x (511+1 ) : 2

  = 4104 x 512 : 2

  =2101248

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

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

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

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

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

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

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

Đặt \(A=1+2+4+.........+4096\)

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

\(\Rightarrow2A-A=8192-1\)

\(\Rightarrow A=8191\)

Đặt  \(S=1+2+4+...+1024+2048+4096\)

       \(S=1+2^1+2^2+2^3+....+2^{10}+2^{11}+2^{12}\)

    \(2S=2+2^2+2^3+....+2^{11}+2^{12}+2^{13}\)

\(2S-S=\left(2+2^2+2^3+....+2^{12}+2^{13}\right)-\left(1+2+2^2+....+2^{11}+2^{12}\right)\)

     \(S=2^{13}-1=8192-1=8191\)

Ta co: 2S=2+1+1/2+1/4+...+1/2048

          2S-S=2+1+1/2+1/4+...+1/2048-1-1/2-1/4-...-1/2048-1/4096

         \(\Rightarrow\)S=2-1/4096 =8191/4096

cảm ơn bạn nha

1/ 2 + 2 = 4

2/ 4 + 4 = 8

3/ 8 + 8 = 16

4/ 16 + 16 = 32

5/ 32 + 32 =64

6/ 64 + 64 =128

7/ 128 + 128 =256

8/  256 + 256 =512

9/ 521 + 512 =1033

10/ 2048 + 2048 =4096

k mình đi

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

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

số số hạng là:

(4096 - 2) : 2 + 1 = 2048

Tổng trên là:

(4096 + 2) . 2048 : 2 = 4196352

SSH:(4096-2):2+1=2048

Tổng:(4096+2)x2048:2=4196352