Từ gt suy ra: -4C= 4¹⁰¹+...+4⁴+4³-4² 

 => -4C+C= 4¹⁰¹-4²-4²+4=4¹⁰¹-28 => C=\(\frac{28-4^{101}}{3}\)

\(C=4-4^2-4^3-...-4^{100}\)

     \(=4-\left(4^2+4^3+...+4^{100}\right)\)

\(\Rightarrow\)\(4C=4^2-\left(4^3+4^4+...+4^{101}\right)\)

\(\Rightarrow\)\(4C-C=3C=2.4^2-4^{101}-4\)

\(\Rightarrow\)\(C=\frac{2.4^2-4^{101}-4}{3}=\frac{28-4^{101}}{3}\)

Ta co:   B= 1 + 3 +3² + 3³ + ....... + 3⁹⁹

                  = (1 + 3) + 3²(1+3) + 3⁴(1 + 3) + ......... + 3⁹⁸(1+3) 

               = (1 + 3)(1 + 3² +3⁴ + ......... + 3⁹⁸)

               = 4(1 + 3² +3⁴ + ........... + 3⁹⁸) \(⋮\)4 

    Vay B \(⋮\)4 

   k cho mk nha

B=(1+3)+(3²+3³)+...+(3⁹⁸+3⁹⁹)

  =(1+3)+3²(1+3)+...+3⁹⁸(1+3)

  =4+3².4+.....+3⁹⁸.4

  =4.(1+3²+...+3⁹⁸)

vì 4 chia hết cho 4 => 4.(1+3²+...+3⁹⁸) chia hết cho 4 => B chia hết cho 4 (điều phải chứng minh)

Ta có: A=2^0+2^1+2^2+2^3+...+2^2010
         =>2A=2+2^2+2^3+2^4+...+2^2011
    =>2A-A=(2+2^2+2^3+...+2^2011)-( 1+2+2^2+2^3+...+2^2010)
    =>A= 2^2011-1

Từ đó ta suy ra A=B (=2^2011-1)
 k nha!

2A=2¹+2²+...+2²⁰¹¹

Suy ra: A=2A-A = (2¹+2²+...+2²⁰¹¹) - (2⁰+2¹+...+2²⁰¹⁰)=2²⁰¹¹-1=B

Vậy: A=B.

Tacos2A=1/2^2+1/2^3+...+1/2^2019.Lấy2A-A=1/2^2019-1/2

1/2 + 1/2^2 + 1/2^3 + 1/2^4 + ... + 1/2^2018 = (2^2018-1)/2^2018

a/ 2^x . 7 = 224

2^x = 224 : 7

2^x = 32

2^x = 2⁵

x = 5.

b/ 3^{2x + 1} . 11 = 2673

3^{2x + 1} = 2673 : 11

3^{2x + 1} = 243

3^{2x + 1} = 3⁵

3^2x = 3^{5 - 1}

3^2x = 3⁴

2x = 4

x = 4 : 2

x = 2.

c/ (3x + 5)² = 289

(3x + 5)² = 17²

3x + 5 = 17

3x = 17 - 5

3x = 12

x = 12 : 3

x = 4.

d/ x . (x²)³ = x⁵

x¹ . x⁵ = x⁵

x⁶ = x⁵

=> x = 0 hoặc x = 1

a) 2^x x 7=224

2^x=224:7

2^x=32

2^x=2⁵

=> x=5

Vậy x=5

b) 3^2x+1 x 11=2673

3^2x+1=2673:11

3^2x+1=243

3^2x+1=3⁵

=> 2x+1=5

x=(5-1):2

x=2

Vậy x=2

c) (3*x+5)²=289

(3*x+5)²=17²

=> 3*x+5=17

x=(17-5):3

x=4

Vậy x=4

d) x.(x²)³=x⁵

x.x⁶=x⁵

x=x⁵:x⁶

x=x^-1

Trả lời:

Ta có : 1.2²= 1.2.2=1.2.(3-1)=1.2.3-1.2

             2.3²= 2.3.3=2.3.(4-1)=2.3.4-2.3

.................................................

             98.99²= 98.99.99=98.99.(100-1)=98.99.100-98.99

A=1.2.3 - 1.2 + 2.3.4 - 2.3 + ... + 98.99.100 - 98.99 hay A=1.2.3 + 2.3.4 +...+ 98.99.100 - (1.2 + 2.3 + ... + 98.99) = B - C

B=1.2.3 + 2.3.4 + ... + 98.99.100

B.4=1.2.3.4 + 2.3.4.(5 - 1) + ... + 98.99.100.(101 - 97)= 98.99.100.101

=> 98.99.100.101:4= 24497550

C=1.2 + 2.3 + ... + 98.99 

C.3=1.2.3 + 2.3.(4 - 1) + ... + 98.99.(100 - 97)= 98.99.100

=> 98.99.100:3= 323400

Vậy A= 24497550 - 323400 = 24174150

@qqqqqqq cảm ơn bạn nhé! (^_^)