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

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

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

Lại có \(5.2^8=\left(2^2+1\right).2^8=2^{10}+2^8\)

Vậy \(S< 5.2^8\)

S=1+2+2^2+2^3+...+2^9​

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

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

S=2^10-1

5.2^8=(2^2+1).2^8=(2^2.2^8)+(1.2^8)=2^10+2^8

Vì 2^10-1<2^10+2^8=> S<5.2^8

Vậy S < 5. 2^8

Ta có: \(S=1+2+2^2+2^3+...+2^9\)

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

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

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

Mặt khác: \(5.2^8=\left(1+2^2\right).2^8=2^8+2^2.2^8=2^8+2^{10}\)

Vì \(2^{10}-1< 2^8+2^{10}\Rightarrow S< 5.2^8\)

ta có ; S=\(1+2+2^2+....+2^9\)

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

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

=> S= \(2^{10}-1\)=1023

mà 5 nhân 2^8=1280 nên

=>S<5 nhân 2^8 

tick cho mình nh pạn (^_^)

S = 1 + 2 + 2² + ... + 2⁹

2S = 2 + 2² + 2³ + ... + 2¹⁰

2S - S = 2¹⁰ - 1

S = 2¹⁰ - 1

<=> 2⁸.2² - 1

<=> 2⁸.3

Vì 2⁸.3 < 2⁸.5 nên S < 2⁸.5

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

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

=>S=2^8.4-1

=>S<5.2^8

S=2^2006-1

5.2^2004=(2.2+1)2^2004=4.2^2004+2^2004=2^2006+2^2004

=>S<5.2^2004

ta có:\(S=1+2+2^2+...+2^{2005}\left(1\right)\)

\(2S=2+2^2+2^3+...+2^{2006}\left(2\right)\)

\(\Rightarrow2S-S=\left(2+2^2+2^3+...+2^{2006}\right)-\left(1+2+2^2+...+2^{2005}\right)\)

\(\Rightarrow S=2^{2006}-1\Rightarrow S=2^2.2^{2004}-1\Rightarrow S=4.2^{2004}-1\Rightarrow S< 5.2^{2004}\)

Chẳng hiểu gì cả

Giải ro  hơn đc ko

Ta có: S=1+2+2²+2³+…+2⁹

=>2S=2+2²+2³+…+2¹⁰

=>2S-S=2+2²+2³+…+2¹⁰-(1+2+2²+2³+…+2⁹)

=>S=2¹⁰-1=2².2⁸-1=4.2⁸-1<4.2⁸<5.2⁸

=>S<5.2⁸

a)S=1+2+2^2+2^3+...+2^9

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

2S-S=(2+2^2+2^3+2^4+...+2^10)-(1+2+2^2+2^3+...+2^9)

S=2^10-1

S=1024-1

S=1023

Ta có:5.2^8=5.256=1280

Mà 1280>1023

=>S<5.2^8

b)Ta có:M=1+2+2^2+2^3+2^4

=>2M=2+2^2+2^3+2^4+2^5

=>2M-M=(2+2^2+2^3+2^4+2^5)-(1+2+2^2+2^3+2^4)

=>M=2^5-1

Mà N=2^5-1

=>M=N

Không biết có bị sai lỗi nào hay không,nhớ kiểm tra đó

a)S = 1 + 2 + 2² + 2³ + 2⁴ +2⁵ +2⁶ +2⁷ + 2⁸ + 2⁹
2S = 2.(1 + 2 + 2² + 2³ + 2⁴ +2⁵ +2⁶ +2⁷ + 2⁸ + 2⁹)

2S = 2 + 2² + 2³ + 2⁴ +2⁵ +2⁶ +2⁷ + 2⁸ + 2⁹ + 2¹⁰

S = (2 + 2² + 2³ + 2⁴ +2⁵ +2⁶ +2⁷ + 2⁸ + 2⁹ + 2¹⁰) - (1 + 2 + 2² + 2³ + 2⁴ +2⁵ +2⁶ +2⁷ + 2⁸ + 2⁹)

S = 2¹⁰ - 1

Suy ra:   S = \(\frac{2^{9+1}-1}{2-1}\)

S = \(\frac{2^{10}-1}{1}\)

S = 2¹⁰ - 1

S = 1023

b)Mình không thể giúp bạn vì mình không rõ 5.2⁸ hay (5.2)⁸