2S = 2+2²+2³+2⁴+...+2¹⁰

2S - S = S = 2¹⁰-1

S = 2⁸.2²-1

S = 2⁸.4 - 1

Ta có:

5.2⁸ > 2⁸.4 > 2⁸.4 - 1

=> 5.2⁸ > 2⁸.4-1

=> P > S

=> S < P

S= \(2^{10}-1\)

\(P=\left(2^2+1\right)2^8=2^{10}+2^8\)

S < P 

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

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

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

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

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

\(\Rightarrow S=2^8.4-1\)

Vì\(4.2^8< 5.2^8\Rightarrow S< 5.2^8\)

Ta có : S = 1 +2¹+2²+........+2²⁰¹⁷

          2S= 2 +2²+2³+.......+2²⁰¹⁸

         2S -S =( 2+2²+2³+......+2²⁰¹⁸) - (1+2+2²+.......+2²⁰¹⁷)

            S = 2²⁰¹⁸-1

            S =2²⁰¹⁸- 1

            S = 2² . 2²⁰¹⁶-1

   \(\Rightarrow\)S < 5. 2²⁰¹⁶

Ta có :S= 1+ 2 + 2² + ........+ 2²⁰¹⁷

Suy ra 2S = 2 + 2² +.......+2²⁰¹⁸

Suy ra 2S -S = (2-2) + (2²-2²)+......+(2²⁰¹⁸ - 1)

Suy ra S=2²⁰¹⁸-1

Suy ra  S ‹ 5.2²⁰¹⁶

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

2S=2(1+2+2²+...+2⁹)

2S=2+2²+...+2¹⁰

2S-S=(2+2²+...+2¹⁰)-(1+2+2²+...+2⁹)

S=2¹⁰-1=1024-1=1023

5*2⁸=5*256=1280.Vì 1280>1023

=>5*2⁸>2¹⁰-1 <=> 5*2⁸>S

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

Iiiiii

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

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

=> \(S=2^{10}-1=1024-1=1023\)

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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