A = 1 + 5 + 5^2 + 5^3 +...+ 5^200

=> 5A=5+5^2+...+5^201

=> 5A-A=(5+5^2+...+5^201)-( 1 + 5 + 5^2 + 5^3 +...+ 5^200)

=> 4A = 5^201-1

=> A=\(\frac{5^{201}-1}{4}\)

Sai đề hay sao ấyNguyễn Lê Nhật Đăng

\(A=1+5+5^2+...+5^{200}\)

\(\Rightarrow5A=5+5^2+5^3+...+5^{201}\)

\(\Rightarrow5A-A=\left(5+5^2+5^3+5^{201}\right)-\left(1+5+5^2+...+5^{200}\right)\)

\(\Rightarrow4A=5^{201}-1\)

\(\Rightarrow A=\frac{5^{201}-1}{4}\)

Vậy \(A=\frac{5^{201}-1}{4}\)

a: =(-1)+(-1)+...+(-1)=-1011

b: =(-5)+(-5)+...+(-5)=-175

`G=1-5+5^{2}-5^{3}+5^{4}-...-5^{199}-5^{200}`

`5G=5-5^{2}+5^{3}-5^{4}+5^{5}-...-5^{200}-5^{201}`

`=>5G+G=1-2.5^{200}-5^{201}`

\(=>G=\dfrac{1-2.5^{200}-5^{201}}{6}\)

a) 2 x 2 = 4              3 x 3 = 9

2 x 4 = 8              3 x 5 = 15

2 x 6 = 12              3 x 7 = 21

2 x 8 = 16              3 x 9 = 27

4 x 4 = 16              5 x 5 = 25

4 x 2 = 8              5 x 7 = 35

4 x 6 = 24              5 x 9 = 45

4 x 8 = 32              5 x 3 = 15

b) 200 x 4 = 800              300 x 2 = 600

200 x 2 = 400             300 x 3 = 900

400 x 2 = 800             500 x 1 = 500

100 x 4 = 400             100 x 3 = 300

Trả lời 1 câu thôi nhé em 100 nhân 4 bằng 400 nhá em

a) 2 x 2 =4 ......              3 x 3 = ..9....

2 x 4 = ....8..              3 x 5 = ...15...

2 x 6 = ....12..              3 x 7 = .21.....

2 x 8 = ..16....              3 x 9 = ..27....

4 x 4 = ...16...              5 x 5 = ...25...

4 x 2 = ...8...              5 x 7 = ..35....

4 x 6 = .....24.              5 x 9 = .45.....

4 x 8 = ..32....              5 x 3 = .15.....

b) 200 x 4 = 800......              300 x 2 =600 ......

200 x 2 = ..400....             300 x 3 = 900......

400 x 2 = .....800.             500 x 1 = ..500....

100 x 4 = ....400..             100 x 3 = .300.....

Lời giải:
Gọi tổng trên là $K$
$K=1+5^2+5^3+5^4+...+5^{200}$

$5K=5+5^3+5^4+5^5+...+5^{201}$
$\Rightarrow 5K-K = 5+5^{201}-1-5^2$

$\Rightarrow 4K = 5^{201}-21$

$\Rightarrow K= \frac{5^{201}-21}{4}$

7 × 3 mu x + 20 × 3 mu x = 3 mu 25

\(A=1+7+7^2+7^3+...+7^{200}\)

\(\Rightarrow7A=7+7^2+7^3+...+7^{201}\)

\(\Rightarrow7A-A=\left(7+7^2+...+7^{201}\right)-\left(1+7+7^2+...+7^{200}\right)\)

\(\Rightarrow6A=7^{201}-1\)

\(\Rightarrow A=\frac{7^{201}-1}{6}\)

\(B=5^1+5^3+5^5+...+5^{101}\)

\(\Rightarrow5^2B=5^3+5^5+5^7+...+5^{103}\)

\(\Rightarrow25B-B=\left(5^3+5^5+...+5^{103}\right)-\left(5+5^3+...+5^{101}\right)\)

\(\Rightarrow24B=5^{103}-5\)

\(\Rightarrow B=\frac{5^{103}-5}{24}\)

\(D=1+a+a^2+a^3+...+a^n\)

\(\Rightarrow aD=a+a^2+a^3+...+a^{n+1}\)

\(\Rightarrow aD-D=\left(a+a^2+...+a^{n+1}\right)-\left(1+a+a^2+...+a^n\right)\)

\(\Rightarrow\left(a-1\right)D=a^{n+1}-1\)

\(\Rightarrow D=\frac{a^{n+1}-1}{a-1}\)

a) 210 -5.x= 200

<=> 5.x    = 210 - 200

<=> 5.x     = 10

<=> x         = 10 : 5

<=> x         = 2

Vậy x = 2

b) 210 - 5 . ( x-10 ) = 200

<=> 5. (x-10)          = 210 - 200

<=> 5.(x-10)           = 10

<=> x -10                = 10 : 5

<=> x - 10              = 2

<=>x                     = 12

Vậy x = 12

d)350 : x + 10 = 20

<=> 350 : x       = 20 - 10

<=> 350 : x         = 10

<=> x                 = 350 : 10

<=> x               = 35

Vậy x = 35

e)36 : ( x - 5 ) = 2²

<=> 36 : ( x-5) = 4

<=> x - 5        = 36 : 4

<=> x - 5          = 9

<=> x                = 9 + 5

<=> x               = 14

Vậy x =14

e) [3 . (70-x) + 5 ] : 2 = 46

<=>  [3 . (70-x) + 5 ]  = 46 . 2 

<=>  [3 . (70-x) + 5 ]  = 92

<=> 210 - 3.x + 5        = 92

<=>210- 3.x              = 92 - 5

<=> 210 - 3.x            = 87

<=> 3.x                       = 210 - 87

<=> 3.x                    = 123

<=> x                      = 123 : 3

<=> x                     = 41

Vậy x = 41