x + 2x + 3x + ...... + 99x = 2 + 4 + 6 + ...... + 198

x*(1+2+3+......+99) = 1*2 + 2*2 + 3*2 + ...... +99*2

x*(1+2+3+.....+99)=  2*(1+2+3+.....+99)

Vậy x = 2

x + 2x + 3x + ... + 99x = 2 + 4 + 6 + 198 (có 99 số hạng)

x + 2x + 3x + ... + 99x = (198 + 2) . 99 : 2 

x .(1 + 2 + 3 + ... + 99) = 9900

x .  [(99 + 1) . 99 : 2]    = 9900

x . 4950                      = 9900

x                                = 9900 : 4950

x                                = 2

x+2x+3x+....+99x=2+4+6+..+198

x(1+2+3+4+...+99)=9900

x=9900/4950

x=2

x + 2x + 3x + 4x + ...... + 99x = 2 + 4 + 6 + 8 + ..... + 198

x.(1 + 2 + 3 + 4 + 5 + ...... + 99) = 2 + 4 + 6 + 8 + ..... + 198 

Ta đưa (1 + 2 + 3 + 4 + 5 + ...... + 99) ; (2 + 4 + 6 + 8 + ..... + 198)  về công thức tính dãy số

=> 1 + 2 + 3 + 4 + 5 + ...... + 99 = 1950

=>  2 + 4 + 6 + 8 + ..... + 198 = 9900

=> x.4950 = 9900

=> x = 2

                                                 a, (-x) = 2015^2015:2015^2015                  => (-x) =1   => x=-1

                                                   b, x = 27                                                             c, x = 2

                                                                           ^_^ Tick nhé ^_^

a, 2015²⁰¹⁵(-x)=2015²⁰¹⁵

=>2015²⁰¹⁵ :2015²⁰¹⁵=-x

=>1=-x

=>x=-1

{ x² - [ 6² - ( 8² - 9.7)³ - 7.5]³ - 5.3 }³ = 1

{ x² + [ 36 - (64 - 63)³ - 35]³ - 15}³ = 1

[ x² - ( 36 - 1³ - 35 ) - 15 ]³ = 1

[ x² - ( 36 - 1 - 35 ) - 15]³ = 1

[ x² - ( 35 - 35 ) - 15]³ = 1

[ x² - 0 - 15]³ = 1

( x² - 15 )³ = 1

<=> ( x² - 15)³ = 1³

=> x² - 15 = 1

<=> x² = 16

=> x = 4

Ta có:

\(D=1.2+2.3+3.4+4.5+...+99.100\)

\(\Leftrightarrow3D=1.2.\left(3-0\right)+2.3+\left(4-1\right)+3.4+\left(5-2\right)+4.5.\left(6-3\right)+...+99.100.\left(101-98\right)\)

\(\Leftrightarrow3D=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+...+99.100.101-98.99.100\)

\(\Leftrightarrow3D=99.100.101\Leftrightarrow D=\frac{99.100.101}{3}=333300\)

\(B=1.3+2.4+3.5+4.6+...+99.101\)

\(\Leftrightarrow B=\left(1.3+3.5+...+99.101\right)+\left(2.4+4.6+...+98.100\right)\)

\(\Leftrightarrow6B=\left(1.3.\left(5-\left(-1\right)\right)+3.5.\left(7-1\right)+...+99.101.\left(103-97\right)\right)+\left(2.4.\left(6-0\right)+4.6.\left(8-2\right)+...+98.100.\left(102-96\right)\right)\)

\(\Leftrightarrow B=\frac{99.101.103+3}{6}+\frac{98.100.102}{6}=338250\)

Vì các bước gần tương tự như bài a) nên mình bỏ bước.

\(C=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\)

\(\Leftrightarrow C=\frac{1}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{48.49.50}\right)\)

\(\Leftrightarrow C=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)\)

\(\Leftrightarrow C=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{49.50}\right)=\frac{1}{2}.\frac{612}{1225}=\frac{306}{1225}\)

a)x+(x+1)+(x+2)+(x+3)+...+(x+99)+(x+100)=5555

=> 101x +5050 = 5555

=> 101x = 505

=> x = 505 : 101 = 5

Vậy, x = 5

b)1+2+3+4+...+x=820

=> ( x+1) x :2 = 820

=> (x+1)x = 1640

Mà 1640 = 40 . 41

=> x = 40 ( vì {x+1} - x = 1)

Vậy, x = 40

c) 3^x+1 = 9.27=243

=> 3^x+1 = 3⁵

=>x + 1 = 5

=> x = 4

Vậy, x=4

d) x+2x+3x+...+99x+100x=15150

=> [( 100 + 1) x 100 :2 ] x = 15150

=> 5050x = 15150

=> x = 15150:5050 = 3

Vậy, x =3

e)(x+1)+(x+2)+(x+3)+...+(x+100)=205550

=> 100x + 5050 = 205550

=> 100x =  205550 - 5050= 200500

=> x =  200500 : 100 = 2005

Vậy, x = 2005

f)3^x+3^x+1+3^x+2=351

=> 3^x + 3^x . 3 + 3^x x 9 = 351

=> 3^x ( 1+3+9) = 351

=> 3^x  . 13 = 351

=> 3^x  = 351 :13=27 mà 27 = 3³

=> x=3

Vậy, x=3

mình đg cần gấp á

a) \(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5555\)

\(\Rightarrow x+x+1+x+2+x+3+...+x+100=5555\)

\(\Rightarrow101\cdot x+5050=5555\)

\(\Rightarrow101\cdot x=5555-5050\)

\(\Rightarrow101\cdot x=505\)

\(\Rightarrow x=505:101\)

\(\Rightarrow x=5\)

b) \(1+2+3+4+...+x=820\)

\(\Rightarrow\left(x+1\right)\cdot\left[\left(x-1\right):1+1\right]:2=820\)

\(\Rightarrow\left(x+1\right)\cdot\left(x+1-1\right):2=820\)

\(\Rightarrow\left(x+1\right)\cdot x:2=820\)

\(\Rightarrow x\cdot\left(x+1\right)=820\cdot2\)

\(\Rightarrow x\cdot\left(x+1\right)=1640\)

Ta thấy: \(40\cdot41=1640\)

Vậy: \(x=40\)

1

a) x = 25 - 16

x = 9

b) 2x = 156-82

2x = 74

x = 74 : 2

x = 37

c) 150 : (18-x) = 150-125

150 : (18-x) = 25

18-x = 150 : 25

18-x = 6

x =18-6

x= 12

d) 6.6 :x = 8-4

36 : x = 4

x =36:4

x = 9

e)(99x-x) : 2+1= 50x

Ta có:

50x + (1+3+5+7+9+.....+99)=75.10.10

50x + (99+1).50:2 =7500

50x + 2500=7500

50x=7500-2500

50x=5000

x =5000:50

x = 100

Tim x € N biet :

a / x + 16 = 25

=> x = 25 - 16

=> x = 9

b / 156 - 2x = 82

=> 2x = 156 - 82

=> 2x = 74

=> x = 37

c / 150 -150 : ( 18 - x ) = 125

=> 150 : ( 18 - x ) = 125 -150

=> 150 : ( 18 - x ) = - 25

=> 18 - x = -6

=> x = 18 - ( -6 )

=> x = 24

d / 6² : x = 2³ - 4

=> 36 : x = 8 - 4

=> 36 : x = 4

=> x = 36 : 4

=> x = 9

e / x + 3x + 5x + ................. +99x = 75 × 10²

^=> x + 3x + 5x +....+ 99x = 7500

=> x. ( 1 + 3 + 5 +....+ 99 ) = 7500

Số các số hạng là : ( 99 - 1 ) : 2 + 1 = 50

=> Số cặp là : 50 : 2 = 25

Ta có:

x. ( 1 + 3 + 5 +....+ 99 ) = 7500

=> x. [ ( 1 + 99 ) + ( 2 + 98 ) +.... ] = 7500

=> x. 100 .25 =7500

=> x. 2500 = 7500

=> x = 7500 : 2500

=> x = 3

a) x = 25 - 16

x = 9

b) 2x = 156-82

2x = 74

x = 74 : 2

x = 37

c) 150 : (18-x) = 150-125

150 : (18-x) = 25

18-x = 150 : 25

18-x = 6

x =18-6

x= 12

d) 6.6 :x = 8-4

36 : x = 4

x =36:4

x = 9

e)(99x-x) : 2+1= 50x

Ta có:

50x + (1+3+5+7+9+.....+99)=75.10.10

50x + (99+1).50:2 =7500

50x + 2500=7500

50x=7500-2500

50x=5000

x =5000:50

x = 100

a . 2x + 48 = 60

     2x = 60 - 48 = 12

     x=12:2=6

b/3.(x+5)+8=80

  3.(x+5)=80-8=72

x+5=72:3

x+5=24

x=24-5=19

c/2x+3x=50

x . ( 2 + 3 ) = 50

x.5=50

x=50:5=10

d/ x +2x+3x+.....+99x+100x=10100

lười suy nghĩ lắm

e/x.(x+2)=0

x=0 bởi vì 0 nhân với số 2 = 0

a) 2x+48=60

=>2x=60-48

=>2x=12

=>x=12:2

x=6

\(a,2x+48=60\) 

               \(2x=60-48\)

                \(2x=12\)

                   \(x=6\)

\(b,3.\left(x+5\right)+8=80\)

      \(3x+15+8=80\)

              \(3x+23=80\)

                         \(3x=80-23\)

                          \(3x=57\)

                             \(x=19\)

\(c,2x+3x=50\)

 \(x.\left(2+3\right)=50\)

                \(5x=50\)

                   \(x=10\)