S = 1 + 2 + 2x2 + 2x2x2 + ... +2x2x..x2 (13 thừ sô nhân 2)

2S = 2 + 2x2 +2x2x2 +..+2x2x2x..x2 (14 thùa số)

2S - S = 2 + 2x 2 + 2x 2x 2 + .. +2x2x2..x2(14 số x2 ) - 1  - 2 - 2x2 - 2x 2 - ... - 2x2x2..x2 ( 13 thừa số nhân 2)

S =  2x2x2x..x2 (14 thùa soos) - 1 

S = 16384 - 1 = 16383

Gọi dãy số : 

2 + 4 + 8 + 16 + 32 +....+ 4096 + 8192 là : A

Đặt A x 2 = 2 + 4 +8 +16 + 32 + ....+ 16384 

Cùng thêm 1 và bớt 1 ta có như sau : 

A x 2 = 1 + 2 + 4 + 8 + 16 + .....+ 1892 + 16384 - 1 

A x 2 = A + 16384 - 1 

A = 16384 -1 

A = 16383 

mk biet lam

Dãy số trên có số số hạng là

         \(\left(8192-2\right):2+1=4096\)

Dạy trên có tổng là

       (2+8192).4096:2=16781312

Đặt A = 1 + 2 + 4 + 8 + 16 + … + 4096 + 8192
Ta có: A = 2⁰ + 2¹ + 2² + 2³ + 2⁴ + … + 2¹² + 2¹³ (1)
Nhân cả hai vế của (1) cho 2, ta được: 2A = 2¹ + 2² + 2³ + 2⁴ + 2⁵ + … + 2¹³ + 2¹⁴ (2)
Lấy (2) - (1), ta được: 2A - A = 2¹ + 2² + 2³ + 2⁴ + 2⁵ + … + 2¹³ + 2¹⁴ - (2⁰ + 2¹ + 2² + 2³+ 2⁴ + … + 2¹² + 2¹³)
A = 2¹ - 2⁰ + 2² - 2¹  + 2³ - 2²  + 2⁴ - 2³ + 2⁵ - 2⁴  + … + 2¹³ - 2¹²  + 2¹⁴  - 2¹³
A = 2¹⁴ - 2⁰
A = 16384 - 1
A = 16383

dãy trên có số chữ số là:

( 8192 - 2 ) : 2 + 1 = 4096

tổng là:

( 2 + 8192 ) x 4096 : 2 = 16781312

2 + 4 + 6 + ... + 8192

= 2 + 4 + 6 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 + 4096 + 8192 = 16382

(Quy luật : Lấy một số nhân với 2 sẽ ra số liền kề nó)

Đặt A = 1 + 2 + 4 + ... + 8192

A = 1 + 2 + 2² + ... + 2¹³

=> 2A = 2 + 2² + 2³ + ... + 2¹⁴

=> 2A - A = ( 2 + 2² + 2³ + ... + 2¹⁴ ) - ( 1 + 2 + 2² + ... + 2¹³ )

<=> A = 2¹⁴ - 1

<=> A = 16383

Vậy A = 16383

16383

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mik nghĩ là bằng 16383 nhung mà ko biết có đúng ko 

đáp án là 16383

chắc chắn 10000000000000000000......%luôn

16383

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

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

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

=>A=2^14-1

8192-1):1+1=8192

tổng:8192+1)x8192:2=33558528

k mik nha

cảm ơn nha

Có 19 con ruồi đậu trên một mặt bàn hình vuông có cạnh 3dm .Chứng tỏ rằng phải có ít nhất 3 con ruồi là ở vị trí 3 đỉnh của một tam giác có diện tích bé hơn 1dm2

= 1 + 2 + 2² + 2³  + ..... + 2¹² + 2¹³

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

= 2 + 2² + 2³ + 2⁴ + .... + 2¹³ + 2¹⁴ - 1 - 2² - 2³ - 2⁴ - ..... - 2¹² - 2¹³

= 2¹⁴ - 1

= 16383

Cảm ơn