\(A=5+5^2+5^3+5^4+...+5^{2004}\)

\(5A=5^2+5^3+5^4+5^5+...+5^{2005}\)

\(5A-A=\left(5^2+5^3+5^4+5^5+...+5^{2005}\right)-\left(5+5^2+5^3+5^4+...+5^{2004}\right)\)

\(4A=5^{2005}-5\)

\(A=\dfrac{5^{2005}-5}{4}\)

\(B=7^1+7^2+7^3+....+7^{2015}\)

\(7B=7^2+7^3+7^4+....+7^{2016}\)

\(7B-B=\left(7^2+7^3+7^4+...+7^{2016}\right)-\left(7+7^2+7^3+....+7^{2015}\right)\)

\(6B=7^{2016}-7\)

\(B=\dfrac{7^{2016}-7}{6}\)

\(C=4^5+4^6+4^7+...+4^{2016}\)

\(4C=4^6+4^7+4^8+...+4^{2017}\)

\(4C-C=\left(4^6+4^7+4^8+...+4^{2017}\right)-\left(4^5+4^6+4^7+...+4^{2016}\right)\)

\(3C=4^{2017}-4^5\)

\(C=\dfrac{4^{2017}-4^5}{3}\)

A = 5 + 5² + 5³ + 5⁴ + ... + 5²⁰⁰⁴

5A = 5² + 5³ + 5⁴ + 5⁵ + ... + 5²⁰⁰⁵

5A - A = 5²⁰⁰⁵ - 5

4A = 5²⁰⁰⁵ - 5

A = (5²⁰⁰⁵ - 5) : 4

B = 7¹ + 7² + 7³ + ... + 7²⁰¹⁵

7B = 7² + 7³ + 7⁴ + ... + 7²⁰¹⁶

7B - B = 7²⁰¹⁶ - 7

6B = 7²⁰¹⁶ - 7

B = (7²⁰¹⁶ - 7) : 6

C = 4⁵ + 4⁶ + 4⁷ + ... + 4²⁰¹⁶

4C = 4⁶ + 4⁷ + 4⁸ + ... + 4²⁰¹⁷

4C - C = 4²⁰¹⁷ - 4⁵

3C = 4²⁰¹⁷ - 4⁵

C = (4²⁰¹⁷ - 4⁵) : 3

a, 4 + \(4^2\) + \(4^3\) + ... + \(4^{60}\) chia hết cho 5

= ( 4 + \(4^2\) ) + ( \(4^3\) + \(4^4\) ) +... + ( \(4^{59}\) + \(4^{60}\))

= ( 4 + \(4^2\) ) + \(4^3\) . ( 4 + \(4^2\) ) +... + \(4^{59}\). ( 4 + \(4^2\) )

= 20 + \(4^3\) . 20 + ... + \(4^{59}\) . 20

= 20 . ( 1 + \(4^3\) + ... + \(4^{59}\) ) chia hết cho 5

4 + \(4^2\) + \(4^3\) + ... + \(4^{60}\) chia hết cho 21

= ( 4 + \(4^2\) + \(4^3\) ) + ( \(4^4\) + \(4^5\) + \(4^6\) ) + ... + ( \(4^{58}\)+ \(4^{59}\) + \(4^{60}\) )

= ( 4 + \(4^2\) + \(4^3\) ) + \(4^4\) . ( 4 + \(4^2\) + \(4^3\) ) + ... + \(4^{58}\) . ( 4 + \(4^2\) + \(4^3\) )

= 84 + \(4^4\) . 84 + .... + \(4^{58}\) . 84

= 84 . ( 1 + \(4^4\) + ... + \(4^{58}\) ) chia hết cho 21

b, 5 + \(5^2\) + \(5^3\) + ... + \(5^{10}\) chia hết cho 6

= ( 5 + \(5^2\) ) + ( \(5^3\) + \(5^4\) ) + ... + ( \(5^9\) + \(5^{10}\) )

= ( 5 + \(5^2\) ) + \(5^3\) . ( 5 + \(5^2\) ) + ... + \(5^9\) . ( 5 + \(5^2\) )

= 30 + \(5^3\) . 30 + ... + \(5^9\) . 30

= 30 . ( 1 + \(5^3\) + ... + \(5^9\) ) chia hết cho 6

[(10x-5).5³]-4.5⁴=5⁴

[(10x-5).5³]-4.5⁴=625

[(10x-5).5³]-4=1

[(10x-5).5³]=5

10x-5=0,04

10x=5,04

x=0,504

\(C=\frac{5}{4}+\frac{5}{4^2}+\frac{5}{4^3}+...+\frac{5}{4^{99}}\)

\(4C=5+\frac{5}{4}+\frac{5}{4^2}+\frac{5}{4^3}+...+\frac{5}{4^{98}}\)

\(4C-C=\left(5+\frac{5}{4}+...+\frac{5}{4^{98}}\right)-\left(\frac{5}{4}+\frac{5}{4^2}+...+\frac{5}{4^{99}}\right)\)

\(3C=5-\frac{5}{4^{99}}\)

\(C=\frac{5-\frac{5}{4^{99}}}{3}\)

\(C=\frac{5}{3}-\frac{5}{4^{99}.3}< C\)

                                đpcm

dễ ẹc!!!!!!!!

a: \(\Leftrightarrow2^x=1024\cdot3+1024\cdot7776+7776\cdot5\)

\(\Leftrightarrow2^x=8004576\)

hay \(x\in\varnothing\)

b: \(\Leftrightarrow x\left(x+3\right)^{100}-\left(x+3\right)^{100}=0\)

\(\Leftrightarrow\left(x+3\right)^{100}\left(x-1\right)=0\)

=>x=-3 hoặc x=1

\(5^x.5^{x+3}=5^4+5^4+5^4+5^4+5^4\\ 5^x\left(1+5^3\right)=5^4\left(1+1+1+1+1\right)\\ 5^x\left(1+125\right)=5^4.5\\ 5^x.126=5^5\\ \dfrac{5^5}{5^x}=126\\ \Rightarrow5-x=126\\ \Rightarrow x=5-126=-121\)

b,

\(24+5x=7^{15}:7^{12}\\ 24+5x=7^3\\ 24+5x=343\\ 5x=343-24\\ 5x=319\\ x=319:5=63,8\)

c,

\(5x-2006=2^4.4\\ 5x-2006=64\\ 5x=64+2006\\ 5x=2017\\ x=2017:5=414\)

B=-4/5+4/5²-4/5³+...+4/5²⁰⁰

5B=-4+4/5-4/5²+...+4/5²⁰¹

5B+B=-4+4/5²⁰⁰

6B=-4x5²⁰⁰/5²⁰⁰+4/5²⁰⁰

6B=-4+4x5²⁰⁰/5²⁰⁰

Còn lại bạn tính nốt nha

thank you

a ) Ta có : 4(x - 5) - 3(x + 7) = -19

<=> 4x - 20 - 3x - 21 = -19

=> x - 41 = -19

=> x = -19 + 41

=> x = 22

b) Ta có " 7(x - 3) - 5(3 - x) = 11x - 5

<=> 7x - 21 - 15 + 5x = 11x - 5

<=> 12x - 36 = 11x - 5

=> 12x - 11x = -5 + 36

=> x = 31 

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