\(S=1+2+2^2+2^3+...+2^9\) 

Đặt \(2S=2+2^2+2^3+2^4+...+2^{10}\) 

\(2S-S=2^{10}-1\) hay \(S=2^{10}-1< 2^{10}\)

\(\Rightarrow\) \(2^{10}=2^2.2^8< 5.2^8\) 

Vậy \(S< 5.2^8\)

\(#Tuyết\)

2S=2+2^2+...+2^10

=>S=2^10-1=1023

5*2^8=256*5=1280

=>S<5*2^8

`@` `\text {Answer}`

`\downarrow`

`S = 1 + 2 + 2^2 + 2^3 + ... + 2^9`

`=> 2S = 2 + 2^2 + 2^3 + ... + 2^10`

`=> 2S - S = (2+2^2 + 2^3 + ... + 2^10) - (1 + 2 + 2^2 + 2^3+...+2^9)`

`=> S = 2^10 - 1`

Mà `2^10 - 1 < 2^10`

`=> S < 2^10 (1)`

Ta có:

 `2^10 = 2^7*8`

Mà `5*2^8 = 5* 2 * 2^7 = 10* 2^7`

Vì `10 > 8 => 2^7 * 8 < 2^7  * 10 (2)`

Từ `(1)` và `(2)`

`=> S < 5 * 2^7``.`

$S=1+2+2^2+...+2^9$

$2S=2\left(1+2+2^2+...+2^{10}\right)$

$2S=2+2^2+2^3+...+2^9$

$2S-S=\left(2+2^2+2^3+...+2^{10}\right)-\left(1+2+2^2+...+2^9\right)$

\(S=2^{10}-1=2^2.2^8-1=4.2^8-1

HT

\(S=1+2+2^2+...+2^9\)

\(S=\dfrac{2^{9+1}-1}{2-1}\)

\(S=2^{10}-1=1023\)

\(5.2^8=5.256=1280>1023\)

\(\Rightarrow S< 5.2^8\)

S < 5. 2^8

2S=2(1+2+2²+2³+..+2⁹)

2S=2+2²+...+2¹⁰

2S-S=(2+2²+...+2¹⁰)-(1+2+2²+2³+..+2⁹)

S=2¹⁰-1 (tới đây tách ra làm như Trinh Hai Nam)

S=2¹⁰-1  

5.2⁸=2¹⁰.1.25  

Vậy S < 5.2⁸

\(2S=2+2^2+2^3+2^4+...+2^{10}\)

=> \(2S-S=\left(2+2^2+2^3+2^4+...+2^{10}\right)-\left(1+2+2^2+2^3+...+2^9\right)\)

=> \(S=2^{10}-1=1024-1=1023\)

Mà \(5.2^8=5.256=1280\)

Vì 1023 < 1280

=> \(S<5.2^8\).

Ta có : 

2S=2+2^2+2^3+...+2^10

2S-S=2+2^2+2^3+...+2^10-1-2-2^2-...-2^9

S=2^10-1

=>S<2^10           (1)

Ta lại có : 

5.2^8>2^10               (2)

Tu (1) va (2) suy ra : S<5.2^8

****

S = 1 + 2 + 2^2 + 2^3 + ... + 2^8

2S = 2(1 + 2 + 2^2 + 2^3 + ... + 2^8)

= 2 + 2^2 + 2^3 + 2^4 + ... + 2^9

2S - S = (2 + 2^2 + 2^3 + 2^4 + ... + 2^9) - (1 + 2 + 2^2 + 2^3 + ... + 2^8)

= 2^9 - 1

=> S = 2^9 - 1

Ta có: 5 . 2^8 = (4 + 1) . 2^8 = 4 . 2^8 + 2^8 = 2^2 . 2^8 + 2^8 = 2^10 + 2^8

Vì 2^9 - 1 < 2^10 + 2^8 => S < 5 . 2^8

tk cho mk nhé các bạn

thank you very much

chúc các bạn học giỏi

\(S=1+2+2^2+2^3+....+2^8+2^9.\)

\(\Rightarrow2S=\text{​​}2+2^2+2^3+....+2^8+2^9+2^{10}\)

\(\Rightarrow2S-S=\left(2+2^2+2^3+....+2^8+2^9+2^{10}\right)-\left(1+2+2^2+2^3+....+2^8+2^9\right)\)

\(S=2^{10}-1=1024-1=1023< 5\cdot2^8=5\cdot256=1280\)

+) Bước 1: Rút gọn S. Ta có: S=\(2^{10}-1\)

+) Bước 2: So sánh.

Ta có: \(2^{10}-1\)\(< 2^{10}=4\cdot2^8< 5\cdot2^8=>2^{10}-1< 2^8\cdot5\left(đpcm\right)\)

HẾT!

Cho S = 1+2+2²+2³+...+2⁹

=> 2S = 2+2²+2³+...+2⁹+2¹⁰

=> 2S - S = S = 2¹⁰ - 1 = 2⁸ . 2² - 1 = 2⁸ . 4 - 1

Ta có 5 . 2⁸ = 4 . 2⁸ + 2⁸

Vì 1 < 2⁸  nên S < 5 . 2⁸

S = 1 + 2 + 2² + 2³ + ..... + 2⁹

2S = 2 + 2² + 2³ + .... + 2⁹ + 2¹⁰

2S - S = ( 2 + 2² + 2³ + .... + 2⁹ + 2¹⁰ ) - ( 1 + 2 + 2² + 2³ + ..... + 2⁹ )

S = 2¹⁰ - 1

Ta có :

5 . 2⁸ = ( 4 + 1 ) . 2⁸ = ( 2² + 1 ) . 2⁸ = 2² . 2⁸ + 1 . 2⁸ = 2¹⁰ + 2⁸

=> 2¹⁰ - 1 < 2¹⁰ + 2⁸

=> S < 2¹⁰  + 2⁸

ta có s=1+2+2^2+2^3+2^4+...+2^9

=>2s=2+2^2+2^3+2^4+...+2^10

=>s=(2^10-1)/2=2^9-1/2

đến đoạn này chắc bn so sánh đc rồi