a: =>1/3*4+1/4*5+...+1/x(x+1)=10/39

=>1/3-1/4+...+1/x-1/x+1=10/39

=>1/3-1/(x+1)=10/39

=>1/(x+1)=13/39-10/39=3/39=1/13

=>x+1=13

=>x=12

b: =>15x=150

=>x=10

c: =>120-5x=45

=>5x=75

=>x=15

`5/3 -2/3 .x=1/2`

`=> 2/3 .x=5/3 -1/2`

`=> 2/3 .x= 10/6 -3/6`

`=> 2/3 .x=7/6`

`=>x=7/6 : 2/3`

`=>x=7/6 xx 3/2`

`=>x=21/12`

`=>x= 7/4`

    3/2.(x-5/3)+4/5=x+1

3/2.x-3/2.5/3+4/5=x+1

          3/2.x-5/2-x=1+4/5

          3/2.x-5/2-x=9/5

                3/2.x-x=9/5+5/2

                   1/2.x=43/10

                         x=43/10:1/2

                         x=43/5

Đề trước đó: 

(x-7)(x+1)-(x-3)^2=(3x-5)(3x+5)-(3x+1)^2+(x-2)^2-x

<=>x^2+x-7x-7-x^2+6x-9=9x^2-25-9x^2-6x-1+x^2-4x+4-x

<=>x^2-11x-6=0

<=>x^2-2x. 11/2 + 121/4-145/4=0

<=>(x-11/2)^2=145/4

<=>|x-11/2|=căn(145)/2

<=>x=[11+-căn(145)]/2

\(\Leftrightarrow2x\left(x+5\right)-3\left(x-2\right)=7x+1\)

\(\Leftrightarrow2x^2+10x-3x+6-7x-1=0\)

\(\Leftrightarrow2x^2+5=0\)(vô lý)

ĐKXĐ:\(\left\{{}\begin{matrix}x\ne2\\x\ne-5\end{matrix}\right.\)

\(\dfrac{2x}{x-2}-\dfrac{3}{x+5}=\dfrac{7x+1}{x^2+3x-10}\\ \Leftrightarrow\dfrac{2x\left(x+5\right)}{\left(x+5\right)\left(x-2\right)}-\dfrac{3\left(x-2\right)}{\left(x+5\right)\left(x-2\right)}=\dfrac{7x+1}{x^2-2x+5x-10}\\ \Leftrightarrow\dfrac{2x^2+10x}{\left(x+5\right)\left(x-2\right)}-\dfrac{3x-6}{\left(x+5\right)\left(x-2\right)}=\dfrac{7x+1}{x\left(x-2\right)+5\left(x-2\right)}\\ \Leftrightarrow\dfrac{2x^2+10x}{\left(x+5\right)\left(x-2\right)}-\dfrac{3x-6}{\left(x+5\right)\left(x-2\right)}-\dfrac{7x+1}{\left(x+5\right)\left(x-2\right)}=0\)

\(\Leftrightarrow\dfrac{2x^2+10x-3x+6-7x-1}{\left(x+5\right)\left(x-2\right)}=0\\ \Leftrightarrow\dfrac{2x^2+5}{\left(x+5\right)\left(x-2\right)}=0\\ \Rightarrow2x^2+5=0\left(vô.lí\right)\)

Vậy pt vô nghiệm

2+6+12+20+...+90

Cách tính mk ko rành lắm xin các anh chị giúp đỡ 

đáp án là : 330

t nha

A = 1 x 2 + 2 x 3 + 3 x 4 + 4 x 5 + ... + 9 x 10

A x 3 = 1 x 2 x 3 + 2 x 3 x 3 + 3 x 4 x 3  + ... + 9 x 10 x 3

A x 3 = 1 x 2 x 3 + 2 x 3 x ( 4 - 1 ) + 3 x 4 ( 5 - 2 ) + ... + 9 x 10 x ( 11 - 8 )

A x 3 = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + 3 x 4 x 5 - 2 x 3 x 4 + 4 x 5 x 6 - 3 x 4 x 5 + ... + 9 x 10 x 11 - 8 x 9 x 10

A x 3 = 9 x 10 x 11

A = 9 x 10 x 11 : 3

A = 330

  Vậy A = 330

Đặt A = 1.2 + 2.3 + 3.4 + 4.5 + ... + 9.10

=> 3A = = 1.2.3 + 2.3.( 4 - 1 ) + 3.4. ( 5 - 2 ) + ... + 9.10.( 11 - 8 )

=> 3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + 3.4.5 - 3.4.5 + ...... + 8.9.10 - 9.10.11

=> 3A = 9.10.11

=> A = 9.10.11 : 3

Vậy A = 330

  Vậy A = 330

Đặt S=

1 x 2 + 2 x 3 + 3 x 4 + 4 x 5 + ............. + 9 x 10 

=>3S + 1.2.3+2.3.3+...+99.100.3

=>1.2.3+2.3(4-1)+3.4(5-2)+...+99.100(101-98)

=>1.2.3+2.3.4-1.2.3+3.4.5+-2.3.4+...+99.100.101-98.100.101

=>99.100.101=999900

=>S=333300

a, 2x3x4x8x25x125= (2x3)x(4x25)x(8x125)= 6x100x1000=600000

b,42/5 +56/9+23/4+3/5+1/3+1/4= (42/5+3/5)+(23/4+1/4)+(56/9+1/3)=9+6+59/9=

a)  2 x 3 x 4 x 8 x 25 x 125=600000

b) 4 2/5 + 5 6/9 + 2 3/4 + 3/5 + 1/3 + 1/4=14

a)  2 x 3 x 4 x 8 x 25 x 125

=(2x3)x(4x25)x(8x125)

=6x100x1000

=600000

b) 4 2/5 + 5 6/9 + 2 3/4 + 3/5 + 1/3 + 1/4

(4+\(\frac{2}{5}\)+\(\frac{3}{5}\))+(5+\(\frac{6}{9}\)+1/3)+(2+\(\frac{3}{4}\)+\(\frac{1}{4}\))

=(4+1)+(5+1)+(2+1)

=5+6+3

=14