Ta có : 
A = 1 + 5 + \(5^2\)+\(5^3\)+...+ \(5^{2023}\)
5A = 5 + \(5^2\)+\(5^3\)+\(5^4\)+..+ \(5^{2024}\)
=> 5A - A = ( 5 + \(5^2\)+\(5^3\)+\(5^4\)+..+ \(5^{2024}\) ) - ( 1 + 5 + \(5^2\)+\(5^3\)+...+ \(5^{2023}\) ) 
=> 4A =  \(5^{2024}\)- 1
Nhận thấy : 
                  \(5^{2024}\) - 1 > ​​​\(5^{2024}\)
=> 4A <  \(5^{2024}\) 
                            Vậy 4A <  \(5^{2024}\) ​

Thấy hay tick hộ mk vs ạ

Bài 1:

$B=1+3+3^2+3^3+...+3^{100}$

$=1+(3+3^2)+(3^3+3^4)+...+(3^{99}+3^{100})$

$=1+3(1+3)+3^3(1+3)+...+3^{99}(1+3)$

$=1+(1+3)(3+3^3+...+3^{99})=1+4(3+3^3+....+3^{99})$

$\Rightarrow B$ chia 4 dư 1.

Bài 2:

$C=5-5^2+5^3-5^4+...+5^{2023}-5^{2024}$

$5C=5^2-5^3+5^4-5^5+...+5^{2024}-5^{2025}$

$\Rightarrow C+5C=5-5^{2025}$

$6C=5-5^{2025}$

$C=\frac{5-5^{2025}}{6}$

\(=60-\dfrac{\left[36+64\right]}{25}\)

\(=60-4=56\)

\(60-[(36+4^3):5^2]\\=60-[(36+64):25]\\=60-(100:25)\\=60-4\\=56\)

60 -[ 36 + 4^3 ) :5^2 

\(=60-(36+64)\div25\)

\(=60-100\div25\)

\(=60-4\)

=56

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

\(2A=2^2+2^3+...+2^{21}\)

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

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

___________

\(B=5+5^2+...+5^{50}\)

\(5B=5^2+5^3+...+5^{51}\)

\(5B-B=5^2+5^3+...+5^{51}-5-5^2-...-5^{50}\)

\(4B=5^{51}-5\)

\(B=\dfrac{5^{51}-5}{4}\)

___________

\(C=1+3+3^2+...+3^{100}\)

\(3C=3+3^2+...+3^{101}\)

\(3C-C=3+3^2+...+3^{101}-1-3-3^2-...-3^{100}\)

\(2C=3^{101}-1\)

\(C=\dfrac{3^{101}-1}{2}\)

2A= 2(2+2²+2³+...+2¹⁹+2²⁰)

2A= 2²+2³+2⁴+...+2²⁰+2²¹

2A-A=(2²+2³+2⁴+...+2²⁰+2²¹)-(2+2²+2³+...+2¹⁹+2²⁰)

A=2²¹-2

Vậy A=2²¹-2

Làm tương tự nhee

khó v

B= 1-2+3-4+5-6+.........+ 51-52+53

b= (1-2)+(2-3)+(5-6)+..........+ (51-52)+53

B= (-1)+(-1)+(-1)+.....+(-1)+53                  ( có 26 số -1)

B= (-26)+ 53

B= 27

a) 13⁴ . 13² = 13⁶

b) 7¹⁶ : 7¹³ = 7³

c) 2⁶ . 2 = 2⁷

d) (5²⁰²³ : 5²⁰¹⁹) . 5² = 5⁴ . 5² = 5⁶

a) \(13^4\cdot13^2=13^{4+2}=13^6\)

b) \(7^{16}:7^{13}=7^{16-13}=7^3\)

c) \(2^6\cdot2=2^{6+1}=2^7\)

d) \(\left(5^{2023}:5^{2019}\right)\cdot5^2\)

\(=5^{2023-2019}\cdot5^2\)

\(=5^2\cdot5^2\)

\(=5^{2+2}=5^4\)

a) Là bằng 13⁶ á

b) Là bằng 7³ á

c) Là bằng 2⁷ á

d) Là bằng 5⁶ á

\(A=5\left(1+5\right)+...+5^{11}\left(1+5\right)\)

\(=6\cdot\left(5+...+5^{11}\right)⋮30\)