=4094

Chúc bạn học tốt ^_^

a=2+2^2+2^3+....+2^11

2a=2^2+2^3+2^4+...+2^12

2a-a=2^2+2^3++2^4+....2^12-2+2^2+2^3+..2^11

a=2^12-2

a=2^10

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

Đặt A = 1 + 2 + 4 + ... + 2048

A = 1 + 2 + 2² + ... + 2¹¹

2A = 2 + 2² + 2³ + ... + 2¹²

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

A = 2¹² - 1

4095

HỌC TỐT

\(2+4+8+16+...+1024+2048=2\left(1+2+4\right)+16\left(1+2+4\right)+128\left(1+2+4\right)+1024\left(1+2\right)=\left(2+16+128+1024\right)\left(1+2+4\right)+3072=1022+3072=4094\)

A = 2+4+8+16+...+1024+2048

=> A =  2 + 2² + 2³ + ... + 2¹¹

=> 2A = 2² + 2³ + 2⁴ ... + 2¹²

=> 2A - A = 2² + 2³ + 2⁴ ... + 2¹² -  2 + 2² + 2³ + ... + 2¹¹

=> A = 2¹² - 2

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

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

2A= 1+ 1/2+ 1/4+...+1/1024

2A-A= ( 1+ 1/2+...+1/1024 ) -  (1/2+1/4+...+2048)

A= 1- 1/2048

A= 2047/2048

Số số hạng là:

( 2048 - 2 ) : 2 + 1 = 1024 ( số )

Tổng là:

( 2048 + 2 ) x 1024 : 2 = 1 049 600

\(A=2+4+8+...+1024+2048\)

\(A=2+2^2+2^3+...+2^{10}+2^{11}\)

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

\(2A-A=2^2+2^3+2^4+...+2^{12}-\left(2+2^2+...+2^{11}\right)\)

\(A=2^{12}-2=4094\)

còn có 1 cách tiểu học nhưng cũng gần giống thế này:

\(A=2+4+8+...+1024+2048\)

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

\(\Rightarrow A+2=4096\Rightarrow A=4094\)