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 thừa số) - 1 

S = 16384 - 1 = 16383

Chúc bạn học tốt....

Sx2=[1+2+4+8+16+32+...+8192]x2

sx2=[2+4+8+16+32+64+...16384]

sx2-s=(2+4+8+16+32+64+...16384)-(1+2+4+8+16+32+...+8192)

s=16384-1

s=16383

A = 1+2+4+8+...+8192

A = 2⁰ + 2¹ + 2² + 2³ +...+2¹³

2A = 2¹+2²+2³+2⁴+...+2¹⁴

2A - A = 2¹⁴ - 2⁰

=> A = 2¹⁴ - 1

        \(A=1+2+4+...+8192\)

           \(=1+2+2^2+2^3+...+2^{13}\)

\(\Rightarrow2A=2+2^2+2^3+2^4+...+2^{13}+2^{14}\)

    \(2A-A=2^{14}-1\)

\(A=2^{14}-1\)

Vậy A = 2¹⁴ - 1.

                                                            Bài giải

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

\(A=1+2+2^2+2^3+2^4+...+2^{13}\)

\(2A=2+2^2+2^3+2^4+2^5+...+2^{14}\)

\(2A-A=2^{14}-1\)

\(A=2^{14}-1\)

thank you 2 bạn cả hai đều làm đúng

\(A=1+2+4+8+16+...+8192\)

\(A=2^0+2^1+2^2+2^3+2^4+....+2^{13}\)

\(2A=2^1+2^2+2^3+2^4+....+2^{14}\)

\(2A-A=\left(2^1+2^2+2^3+2^4+...+2^{14}\right)-\left(2^0+2^1+2^2+2^3+2^4+...+2^{13}\right)\)

\(\Rightarrow A=2^{14}-1=16383\)

2A=2+4+8+..+16384

    =2^1+2^2+...+2^14

Suy ra 2A-A=A=2^14-1

=16384-1=16383

A=1+2+4+8+...+8192

2A=2+4+8+16+...+16284

2A—A=(2+4+8+16+...+16284)—(1+2+4+8+...+8192)

A=16284—1

A=16283

dãy trên có quy luật các số cách đều nhau 2 đơn vị tính số các số hạng rồi nhóm cặp số đầu số cuỗi

1+2+4+8+16+32+64+128+256+512+1024+2048+4096+8192=16383

Đặt A = 1+2+4+..........+8192

A = \(2^0+2^1+......+2^{13}\)

2A = \(2+2^2+....+2^{14}\)

2A - A = \(\left(2-2\right)+\left(2^2-2^2\right)+......+\left(2^{13}-2^{13}\right)+2^{14}-1\)

A = \(2^{14}-1\)

Vào câu hỏi tương tự nha bn.

a﴿Tổng trên có:﴾100‐7﴿:3+1=32﴾số hạng﴿

b﴿Gọi số hạng thứ 22 cửa tổng trên là n

Theo đề bài ta có :

﴾n‐7﴿:3+1=22 ﴾n‐7﴿:3 

   =22‐1 ﴾n‐7﴿:3  

  =21 n‐7      

   =21.3 n‐7     

    =63 n         

   =63+7 n         

   =70 Vậy số hạng thứ 2 của tổng trên là 70

c﴿ Tổng S là:

﴾100+7﴿.32:2=3424

a) tổng trên có số số hạng là :

(  100 - 7 ) : 3 + 1 = 32 ( số )

b ) S là dãy số cách đều tăng dần có khoảng cách 2 số liên tiếp là 3  

Số hạng thứ 22 là :

7 + 3 . ( 22 - 1 ) = 70

c) tổng S là :

( 100 + 7 ) x 32 : 2 = 3424

Đáp số : a ) 32 số

             b ) 90

             c ) 3424

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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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