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

\(a,210-5\left(x-11\right)=200\\ \Rightarrow5\left(x-11\right)=10\\ \Rightarrow x-11=2\\ \Rightarrow x=13.\\ b,\left(2x+1\right):7=2^2+3^2\\ \Rightarrow\left(2x+1\right):7=4+9\\ \Rightarrow\left(2x+1\right):7=13\\ \Rightarrow2x+1=91\\ \Rightarrow2x=90\\ \Rightarrow x=45.\\ c,450:\left[41-\left(2x-5\right)\right]=3^2.5\\ \Rightarrow450:\left[41-\left(2x-5\right)\right]=45\\ \Rightarrow41-\left(2x-5\right)=10\\ \Rightarrow2x-5=31\\ \Rightarrow2x=36\\ \Rightarrow x=18.\\ d,\left(5x-9\right).7+3=80\\ \Rightarrow\left(5x-9\right).7=77\\ \Rightarrow5x-9=11\\ \Rightarrow5x=20\\ \Rightarrow x=4.\)

a) \(210-5\left(x-11\right)=200\)

\(5.\left(x-11\right)=210-200\)

\(5.\left(x-11\right)=10\)

\(x-11=10:5\)

\(x-11=2\)

\(x=2+11\)

\(x=13\)

b) \(\left(2x+1\right):7=2^2+3^2\)

\(\left(2x+1\right):7=13\)

\(2x+1=13.7\)

\(2x=91-1\)

\(2x=90\)

\(x=90:2\)

\(x=45\)

c) \(450:\left[41-\left(2x-5\right)\right]=3^2.5\)

\(450:\left[41-\left(2x-5\right)\right]=45\)

\(\left[41-\left(2x-5\right)\right]=450:45\)

\(\left[41-\left(2x-5\right)\right]=10\)

\(2x-5=41-10\)

\(2x-5=31\)

\(2x=31+5\)

\(2x=36\)

\(x=36:2\)

\(x=18\)

d) \(\left(5x-9\right).7+3=80\)

\(\left(5x-9\right).7=80-3\)

\(5x-9=77:7\)

\(5x-9=11\)

\(5x=11+9\)

\(5x=20\)

\(x=20:5\)

\(x=4\)

oki

\(D=-\dfrac{4}{5}+\dfrac{4}{5^2}-\dfrac{4}{5^3}+...+\dfrac{4}{5^{200}}\)

\(\Rightarrow D=4\left(-\dfrac{1}{5}+\dfrac{1}{5^2}-\dfrac{1}{5^3}+...+\dfrac{1}{5^{200}}\right)\)

\(5D=4\cdot\left(-1+\dfrac{1}{5}-\dfrac{1}{5^2}+...+\dfrac{1}{5^{199}}\right)\)

\(\Rightarrow5D+D=4\cdot\left(-1+\dfrac{1}{5}-\dfrac{1}{5^2}+...+\dfrac{1}{5^{199}}-\dfrac{1}{5}+\dfrac{1}{5^2}-\dfrac{1}{5^3}+...+\dfrac{1}{5^{200}}\right)\)

\(\Rightarrow6D=4\cdot\left(\dfrac{1}{5^{200}}-1\right)\)

\(\Rightarrow D=\dfrac{2}{3}\cdot\left(\dfrac{1}{5^{200}}-1\right)\)

a)
A = 2 + 2² + 2³ + 2⁴ + ... + 2²⁰⁰
2A = 2² + 2³ + 2⁴ + 2⁵ + ... + 2²⁰⁰
2A - A = A = 2²⁰⁰ - 2
b) chịu
c) 
C = 4 + 4² + 4³ + 4⁴ +... + 4¹⁰⁰
4C = 4² + 4³ + 4⁴ + 4⁵ + ... + 4¹⁰¹
4C - C = 3C = 4¹⁰¹ -  4
\(\Rightarrow\)  C = \(\frac{4^{101}-4}{3}\)
d)
D = 5 + 5² + 5³ + ... + 5¹⁰⁰
5D = 5² + 5³ + 5⁴ + ... + 5¹⁰¹
5D - D = 4D = 5¹⁰¹ - 5
\(\Rightarrow\)D = \(\frac{5^{101}-5}{4}\)
 

a: 2x(x+1)-135=-200

=>2(x^2+x)=-65

=>2x^2+2x+65=0

=>x^2+x+32,5=0

=>x^2+x+0,25+32,25=0

=>(x+0,5)^2+32,25=0(vô lý)

b: 4x-5(x-1)+15=13

=>4x-5x+5=-2

=>5-x=-2

=>x=5+2=7

c: 2/3x-1/4=3/5-7/8

=>2/3x=3/5-7/8+1/4=24/40-35/40+10/40=-1/40

=>x=-1/40:2/3=-1/40*3/2=-3/80

d: 1/2(2x-3)+105/2=-137/2

=>1/2(2x-3)=-137/2-105/2=-242/2=-121

=>2x-3=-242

=>2x=-239

=>x=-239/2

= (1 + 199) - (2+198) - ... - 200

= 200 - 200 - .... - 200

= 0

Bài này có phải bằng -100 không hè ai có kết quả giống mình thì mình sẽ k cho

=(200-1):1+1

=200

a) 3A = 3 + 3^2 + 3^3 + 3^4 + ... + 3^100 + 3^ 101
=> 3A - A = (3 + 3^2 + 3^3 + 3^4 + ... + 3^100 + 3^ 101) - (1 + 3 + 3 ^2 + 3 ^ 3 + ... + 3 ^100)
=> 2A = 3^101 - 1 => A = (3^101 - 1)/2
b) 4B = 4 + 4 ^ 2 + 4 ^3 + 4 ^ 4 + ... + 4 ^ 100 + 4^ 101
=> 4B - B = (4 + 4 ^ 2 + 4 ^3 + 4 ^ 4 + ... + 4 ^ 100 + 4^ 101) - (1 + 4 + 4 ^ 2 + 4 ^3 + 4 ^ 4 + ... + 4 ^ 100 )
=> 3B = 4^101 - 1 => B = ( 4^101 - 1)/2
c) xem lại đề ý c xem quy luật như thế nào nhé.
d) 3D = 3^101 + 3^ 102 + 3^ 103 + ... + 36 150 + 3^ 151
=> 3D - D = (3^101 + 3^ 102 + 3^ 103 + ... + 36 150 + 3^ 151) - (3 ^100 + 3 ^ 101 + 3 ^ 102 + .... + 3 ^ 150)
=> 2D = 3^ 151 - 3^100 => D = ( 3^ 151 - 3^100)/2

a) Có A=\(1+3+3^2+3^3+....+3^{100}\)

\(\Rightarrow\)3A =\(3\left(1+3+3^2+3^3+...+3^{100}\right)\)=\(3+3^2+3^3+3^4+...+3^{101}\)

\(\Rightarrow2A=3+3^2+3^3+....+3^{101}-1-3-3^2-3^3-....-3^{100}=3^{101}-1\)\(\Rightarrow A=\dfrac{3^{101}-1}{2}\)

Bài b/c/d : bn cứ lm tương tự.