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 (^_^)

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

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

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

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

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+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 + ..... + 2⁹

=> 2S = 2 + 2² + ..... + 2¹⁰

=> 2S - S = 2¹⁰ - 1

=> S = 2¹⁰ - 1

Lại có : 5.2⁸

= (4 + 1).2⁸

= 2¹⁰ + 2⁸

Nên S <  5.2⁸ 

Cần câu trả lời gấp

Chờ chút nhé

Ta có 2S=2+22+23+....+210

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

=>S<210(1)

Ta lại có: 5.28>4.28 mà 4.28=22.28=210 =>5.28>210(2) Từ (1) và (2)=>S<5.28

Ta có

2S=2+2²+2³+....+2¹⁰

2S-S=2+2²+2³+...+2¹⁰-1-2-2²-....-2⁹

S=2¹⁰-1 =>S<2¹⁰(*)

Ta lại có: 5.2⁸>4.2⁸ mà 4.2⁸=2².2⁸=2¹⁰

=>5.2⁸>2¹⁰(**)

Từ (*) và (**) suy ra S<5.2⁸

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

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

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