S = 2 + 2³ + ... + 2²¹

=> 4S = 2³ + 2⁵ + ... + 2²³

=> 4S - S = 2²³ - 2

=> S = \(\frac{2^{23}-2}{3}\)

Theo bài ra: 2².S = 4.\(\frac{2^{23}-2}{3}\)=11184808

(2^2 + 2) + (2^3 + 2^4) +...........+(2^11 + 1)

= 2. (2+1) + 2^3. (2+1) + ........ + 2^9.(2+1) +(2^11+1)

= 2. 3 + 2^3. 3 + ..... + 2^9. 3 + (2^11 +1)

Vì 3 chia hết cho 3 

=> A chia hết cho 3

\(S=1+2+2^2+2^3+...+2^{2022}\)

\(\Rightarrow2S=2+2^2+2^3+2^4+...+2^{2022}+2^{2023}\)

trừ vế với vế ta được : 

\(2S-S=2^{2023}-1\)

\(\Rightarrow S=2^{2023}-1\)

Ta có:  2E= 2+2^2+2^3+2^4+...+2^10

2E - E = (2+2^2+2^3+2^4+...+2^10) - (1+2+2^2+2^3+...+2^9)

E = 2^10-1

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

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

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

=>\(E=2^{10}-1=1024-1=1023\)

\(A=4+2^2+2^3+..+2^{20}\)

\(\Rightarrow2A=8+2^3+2^4+...+2^{21}\)

\(\Rightarrow2A-A=\left(2^3+2^3+....+2^{21}\right)-\left(2+2+2^2+...+2^{20}\right)\)

\(\Rightarrow A=\left(2^3+2^{21}\right)-\left(2+2+2^2\right)\)

\(\Rightarrow A=2^{21}+8-8\)

\(\Rightarrow A=2^{21}\)

=2162688 nha

Chứng minh cái gì hả bạn?

bn viết cái j mk ko hiểu

Bạn ấy viết như thế này nè :

2 - 2² + 2³ - 2⁴+...+2⁶⁹

\(\text{Đặt A=}2-2^2+2^3-2^4+...+2^{69}\)

\(-2A=2^2+2^3-2^4+2^5-...-2^{70}\)

\(-2A-A\left(-2^2+2^3-2^4+2^5-...-2^{70}\right)-\left(2-2^2+2^3-2^4+..+22^{69}\right)\)

\(-3A=-2-2^{70}\)

\(A=\frac{2+2^{70}}{3}\)

A=

       S = 1 +  2 + 2² + 2³ +...+ 2⁹

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

2S - S =        2¹⁰ - 1

        S =  2¹⁰ - 1

        P = 5.2⁰ = 5 <  7 = 2³ - 1 < 2¹⁰ -1   = S
S > P  

ai nhanh mik tích cho nhé