\(S=1+2+2^2+2^3+...+2^9\) 

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 + 2² + ... + 2⁹

=> 2S = 2 + 2² + ... + 2¹⁰

=> 2S - S = 2¹⁰ - 1

=> S = 2¹⁰ - 1

Ta có : 2¹⁰ = 2².2⁸

=> 2².2⁸ - 1 = 4.2⁸ - 1 < 5.2⁸

Vậy S < 5.2⁸

\(S=2^0+2+2^2+...+2^9\)

Ta có phép tính : \(5\times28=140\)

Mà ta thấy : \(2^9>140\Rightarrow2^0+2+2^2+...+2^9>140\)

\(\Rightarrow S>5.28\)

Ta có:

\(5.28=140\)

Mà \(2^9=512>140\)

\(\Rightarrow2^0+2^1+2^2+2^3+...+2^9>5.28\)

~ Rất vui vì giúp đc bn ~

Ta có : 

\(S=\frac{1}{51}+\frac{1}{52}+\frac{1}{53}+...+\frac{1}{100}>\frac{1}{100}+\frac{1}{100}+\frac{1}{100}+...+\frac{1}{100}=50.\frac{1}{100}=\frac{50}{100}=\frac{1}{2}\)

\(\Rightarrow\)\(S>\frac{1}{2}\)

Vậy \(S>\frac{1}{2}\)

Chúc bạn học tốt ~

\(S>\frac{1}{100}\cdot50=\frac{1}{2}\)

vì\(\frac{1}{51}>\frac{1}{52}>....>\frac{1}{100}\)

=>\(\frac{1}{51}+\frac{1}{52}+...+\frac{1}{100}\)> 50x1/100=1/2(dpcm)

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

=>2S-S=2^10-1

=>S=2^8.4-1

=>S<5.2^8

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

\(\Rightarrow2S=2+2^2+2^3+...+2^{10}\)

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

\(\Rightarrow S=2^{10}-1< 2^{10}=2^7.2^3=2^7.8\)

Do \(5.2^8=5.2.2^7=10.2^7>2^7.8\) nên \(5.2^8>2^{10}>2^{10}-1\)

\(\Rightarrow5.2^8>2^{10}-1\)

Vậy \(5.2^8>2^{10}-1\)

S = 1 + 2 + 2² + 2³ + ... + 2⁹

2S = 2 + 2² + 2³ + 2⁴ + ... + 2¹⁰

2S - S = (2 + 2² + 2³ + 2⁴ + ... + 2¹⁰) - (1 + 2 + 2² + 2³ + ... + 2⁹)

S = 2¹⁰ - 1 < 2¹⁰ = 2².2⁸ = 4.2⁸ < 5.2⁸

=> S < 5.2⁸

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

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