Ta co : 

\(S=1+2+2^2+2^3+...+2^9\)

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

\(5.2^8=\left(2.2+1\right)2^8=4.2^8+2^8=2^{10}+2^8\)

Vay \(S<5.2^8\)

bài này hình

như trong sách

mình cũng cõ

để mình

xem nhé

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

\(S=1+2+2^2+2^3+....+2^8+2^9.\)

\(\Rightarrow2S=\text{​​}2+2^2+2^3+....+2^8+2^9+2^{10}\)

\(\Rightarrow2S-S=\left(2+2^2+2^3+....+2^8+2^9+2^{10}\right)-\left(1+2+2^2+2^3+....+2^8+2^9\right)\)

\(S=2^{10}-1=1024-1=1023< 5\cdot2^8=5\cdot256=1280\)

+) Bước 1: Rút gọn S. Ta có: S=\(2^{10}-1\)

+) Bước 2: So sánh.

Ta có: \(2^{10}-1\)\(< 2^{10}=4\cdot2^8< 5\cdot2^8=>2^{10}-1< 2^8\cdot5\left(đpcm\right)\)

HẾT!

Cho S = 1+2+2²+2³+...+2⁹

=> 2S = 2+2²+2³+...+2⁹+2¹⁰

=> 2S - S = S = 2¹⁰ - 1 = 2⁸ . 2² - 1 = 2⁸ . 4 - 1

Ta có 5 . 2⁸ = 4 . 2⁸ + 2⁸

Vì 1 < 2⁸  nên 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

****

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

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

2S-S=2^10-1

=>S=2^10-1

      =1024-1

      =1023

5.2^8=5.256=1280

Vì 1023<1280=>S<5.2^8

1+2+2²+2³+2⁴+.........+2⁹

2S= 2+2²+2³+2⁴+........+2⁹+2¹⁰

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

S= 2¹⁰-1

Ta có: 5.2⁸= (4+1).2⁸

                 = 4.2⁸+ 2⁸

                    = 2².2⁸+2⁸

                = 2¹⁰+2⁸

=> 2¹⁰-1 < 2¹⁰+2⁸

Hay S < 5.2⁸

\(S=1+2+2^2+2^3+...+2^9\)

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

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

\(S=2^{10}-1< 2^{10}=2^2.2^8=4.2^8< 5.2^8\)