P = 5.2⁸ chứ

bài giải đây nè

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

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

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

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

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

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

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

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

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

\(S=2^{10}-1=2^8.4-1<2^8.5\)

Haha.chắc vậy quá :))

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

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

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

=> \(S=2^{10}-1=1024-1=1023\)

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

****

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

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

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

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

+) 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!