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

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

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

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

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

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

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

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

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

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=1+2+2²+2³+......+2⁹       

=>2S=2+2²+2³+...+2¹⁰

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

=>S=2+2²+2³+...+2¹⁰-1-2-2²-2³-...-2⁹

S=2¹⁰-1

ta có : (4+1).2⁸=4.2⁸+2⁸=2².2⁸+2⁸=2¹⁰+2⁸

=>2¹⁰-1<2¹⁰+2⁸ hay

S<5.2⁸

S = 1 + 2 + 2² + 2³ + ...... + 2⁹       

=> 2S = 2 + 2² + 2³ + ... + 2¹⁰

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

=> S = 2 + 2² + 2³ + ... + 2¹⁰ - 1 - 2 - 2² - 2³ - ... -2⁹

S = 2¹⁰ - 1

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

=> 2¹⁰ - 1 < 2¹⁰ + 2⁸ hay S < 5 . 2⁸

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 + 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

a) S= 1+2+2²+...+2⁹

2S=2+2²+2³+...+2¹⁰

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

S=2¹⁰-1

5.2⁸=2.2+1.2⁸=1+2².2⁸=1+2¹⁰

=>S=5.2⁸

b) A=1+2+2²+....+2¹⁰⁰

2A=2+2²+2³+...+2¹⁰¹

2A-A=(2+2²+2³+...+2¹⁰¹)-(1+2+2²+...+2¹⁰⁰)

A=2¹⁰¹-1

=> A<2¹⁰¹